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Sample records for regularized long-wave equation

  1. Applications of exact traveling wave solutions of Modified Liouville and the Symmetric Regularized Long Wave equations via two new techniques

    Science.gov (United States)

    Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

    2018-06-01

    In this current work, we employ novel methods to find the exact travelling wave solutions of Modified Liouville equation and the Symmetric Regularized Long Wave equation, which are called extended simple equation and exp(-Ψ(ξ))-expansion methods. By assigning the different values to the parameters, different types of the solitary wave solutions are derived from the exact traveling wave solutions, which shows the efficiency and precision of our methods. Some solutions have been represented by graphical. The obtained results have several applications in physical science.

  2. Numerical simulation of the regularized long wave equation by He's homotopy perturbation method

    International Nuclear Information System (INIS)

    Inc, Mustafa; Ugurlu, Yavuz

    2007-01-01

    In this Letter, we present the homotopy perturbation method (shortly HPM) for obtaining the numerical solution of the RLW equation. We obtain the exact and numerical solutions of the Regularized Long Wave (RLW) equation for certain initial condition. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of other methods have led us to significant consequences. The numerical solutions are compared with the known analytical solutions

  3. Numerical simulation of the regularized long wave equation by He's homotopy perturbation method

    Energy Technology Data Exchange (ETDEWEB)

    Inc, Mustafa [Department of Mathematics, Firat University, 23119 Elazig (Turkey)], E-mail: minc@firat.edu.tr; Ugurlu, Yavuz [Department of Mathematics, Firat University, 23119 Elazig (Turkey)

    2007-09-17

    In this Letter, we present the homotopy perturbation method (shortly HPM) for obtaining the numerical solution of the RLW equation. We obtain the exact and numerical solutions of the Regularized Long Wave (RLW) equation for certain initial condition. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of other methods have led us to significant consequences. The numerical solutions are compared with the known analytical solutions.

  4. The Method of Lines Solution of the Regularized Long-Wave Equation Using Runge-Kutta Time Discretization Method

    Directory of Open Access Journals (Sweden)

    H. O. Bakodah

    2013-01-01

    Full Text Available A method of lines approach to the numerical solution of nonlinear wave equations typified by the regularized long wave (RLW is presented. The method developed uses a finite differences discretization to the space. Solution of the resulting system was obtained by applying fourth Runge-Kutta time discretization method. Using Von Neumann stability analysis, it is shown that the proposed method is marginally stable. To test the accuracy of the method some numerical experiments on test problems are presented. Test problems including solitary wave motion, two-solitary wave interaction, and the temporal evaluation of a Maxwellian initial pulse are studied. The accuracy of the present method is tested with and error norms and the conservation properties of mass, energy, and momentum under the RLW equation.

  5. Traveling waves of the regularized short pulse equation

    International Nuclear Information System (INIS)

    Shen, Y; Horikis, T P; Kevrekidis, P G; Frantzeskakis, D J

    2014-01-01

    The properties of the so-called regularized short pulse equation (RSPE) are explored with a particular focus on the traveling wave solutions of this model. We theoretically analyze and numerically evolve two sets of such solutions. First, using a fixed point iteration scheme, we numerically integrate the equation to find solitary waves. It is found that these solutions are well approximated by a finite sum of hyperbolic secants powers. The dependence of the soliton's parameters (height, width, etc) to the parameters of the equation is also investigated. Second, by developing a multiple scale reduction of the RSPE to the nonlinear Schrödinger equation, we are able to construct (both standing and traveling) envelope wave breather type solutions of the former, based on the solitary wave structures of the latter. Both the regular and the breathing traveling wave solutions identified are found to be robust and should thus be amenable to observations in the form of few optical cycle pulses. (paper)

  6. A Galerkin Finite Element Method for Numerical Solutions of the Modified Regularized Long Wave Equation

    Directory of Open Access Journals (Sweden)

    Liquan Mei

    2014-01-01

    Full Text Available A Galerkin method for a modified regularized long wave equation is studied using finite elements in space, the Crank-Nicolson scheme, and the Runge-Kutta scheme in time. In addition, an extrapolation technique is used to transform a nonlinear system into a linear system in order to improve the time accuracy of this method. A Fourier stability analysis for the method is shown to be marginally stable. Three invariants of motion are investigated. Numerical experiments are presented to check the theoretical study of this method.

  7. Benney's long wave equations

    International Nuclear Information System (INIS)

    Lebedev, D.R.

    1979-01-01

    Benney's equations of motion of incompressible nonviscous fluid with free surface in the approximation of long waves are analyzed. The connection between the Lie algebra of Hamilton plane vector fields and the Benney's momentum equations is shown

  8. Hidden regularity for a strongly nonlinear wave equation

    International Nuclear Information System (INIS)

    Rivera, J.E.M.

    1988-08-01

    The nonlinear wave equation u''-Δu+f(u)=v in Q=Ωx]0,T[;u(0)=u 0 ,u'(0)=u 1 in Ω; u(x,t)=0 on Σ= Γx]0,T[ where f is a continuous function satisfying, lim |s| sup →+∞ f(s)/s>-∞, and Ω is a bounded domain of R n with smooth boundary Γ, is analysed. It is shown that there exist a solution for the presented nonlinear wave equation that satisfies the regularity condition: |∂u/∂ η|ε L 2 (Σ). Moreover, it is shown that there exist a constant C>0 such that, |∂u/∂ η|≤c{ E(0)+|v| 2 Q }. (author) [pt

  9. Travelling wave solutions of generalized coupled Zakharov–Kuznetsov and dispersive long wave equations

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    M. Arshad

    Full Text Available In this manuscript, we constructed different form of new exact solutions of generalized coupled Zakharov–Kuznetsov and dispersive long wave equations by utilizing the modified extended direct algebraic method. New exact traveling wave solutions for both equations are obtained in the form of soliton, periodic, bright, and dark solitary wave solutions. There are many applications of the present traveling wave solutions in physics and furthermore, a wide class of coupled nonlinear evolution equations can be solved by this method. Keywords: Traveling wave solutions, Elliptic solutions, Generalized coupled Zakharov–Kuznetsov equation, Dispersive long wave equation, Modified extended direct algebraic method

  10. On a functional equation related to the intermediate long wave equation

    International Nuclear Information System (INIS)

    Hone, A N W; Novikov, V S

    2004-01-01

    We resolve an open problem stated by Ablowitz et al (1982 J. Phys. A: Math. Gen. 15 781) concerning the integral operator appearing in the intermediate long wave equation. We explain how this is resolved using the perturbative symmetry approach introduced by one of us with Mikhailov. By solving a certain functional equation, we prove that the intermediate long wave equation and the Benjamin-Ono equation are the unique integrable cases within a particular class of integro-differential equations. Furthermore, we explain how the perturbative symmetry approach is naturally extended to treat equations on a periodic domain. (letter to the editor)

  11. The modified extended Fan's sub-equation method and its application to (2 + 1)-dimensional dispersive long wave equation

    International Nuclear Information System (INIS)

    Yomba, Emmanuel

    2005-01-01

    By using a modified extended Fan's sub-equation method, we have obtained new and more general solutions including a series of non-travelling wave and coefficient function solutions namely: soliton-like solutions, triangular-like solutions, single and combined non-degenerative Jacobi elliptic wave function-like solutions for the (2 + 1)-dimensional dispersive long wave equation. The most important achievement of this method lies on the fact that, we have succeeded in one move to give all the solutions which can be previously obtained by application of at least four methods (method using Riccati equation, or first kind elliptic equation, or auxiliary ordinary equation, or generalized Riccati equation as mapping equation)

  12. The extended hyperbolic function method and exact solutions of the long-short wave resonance equations

    International Nuclear Information System (INIS)

    Shang Yadong

    2008-01-01

    The extended hyperbolic functions method for nonlinear wave equations is presented. Based on this method, we obtain a multiple exact explicit solutions for the nonlinear evolution equations which describe the resonance interaction between the long wave and the short wave. The solutions obtained in this paper include (a) the solitary wave solutions of bell-type for S and L, (b) the solitary wave solutions of kink-type for S and bell-type for L, (c) the solitary wave solutions of a compound of the bell-type and the kink-type for S and L, (d) the singular travelling wave solutions, (e) periodic travelling wave solutions of triangle function types, and solitary wave solutions of rational function types. The variety of structure to the exact solutions of the long-short wave equation is illustrated. The methods presented here can also be used to obtain exact solutions of nonlinear wave equations in n dimensions

  13. To the complete integrability of long-wave short-wave interaction equations

    International Nuclear Information System (INIS)

    Roy Chowdhury, A.; Chanda, P.K.

    1984-10-01

    We show that the non-linear partial differential equations governing the interaction of long and short waves are completely integrable. The methodology we use is that of Ablowitz et al. though in the last section of our paper we have discussed the problem also in the light of the procedure due to Weiss et al. and have obtained a Baecklund transformation. (author)

  14. Generalized internal long wave equations: construction, hamiltonian structure and conservation laws

    International Nuclear Information System (INIS)

    Lebedev, D.R.

    1982-01-01

    Some aspects of the theory of the internal long-wave equations (ILW) are considered. A general class of the ILW type equations is constructed by means of the Zakharov-Shabat ''dressing'' method. Hamiltonian structure and infinite numbers of conservation laws are introduced. The considered equations are shown to be Hamiltonian in the so-called second Hamiltonian structu

  15. Explicit and exact solutions for a generalized long-short wave resonance equations with strong nonlinear term

    International Nuclear Information System (INIS)

    Shang Yadong

    2005-01-01

    In this paper, the evolution equations with strong nonlinear term describing the resonance interaction between the long wave and the short wave are studied. Firstly, based on the qualitative theory and bifurcation theory of planar dynamical systems, all of the explicit and exact solutions of solitary waves are obtained by qualitative seeking the homoclinic and heteroclinic orbits for a class of Lienard equations. Then the singular travelling wave solutions, periodic travelling wave solutions of triangle functions type are also obtained on the basis of the relationships between the hyperbolic functions and that between the hyperbolic functions with the triangle functions. The varieties of structure of exact solutions of the generalized long-short wave equation with strong nonlinear term are illustrated. The methods presented here also suitable for obtaining exact solutions of nonlinear wave equations in multidimensions

  16. A regularization of the Burgers equation using a filtered convective velocity

    International Nuclear Information System (INIS)

    Norgard, Greg; Mohseni, Kamran

    2008-01-01

    This paper examines the properties of a regularization of the Burgers equation in one and multiple dimensions using a filtered convective velocity, which we have dubbed as the convectively filtered Burgers (CFB) equation. A physical motivation behind the filtering technique is presented. An existence and uniqueness theorem for multiple dimensions and a general class of filters is proven. Multiple invariants of motion are found for the CFB equation which are shown to be shared with the viscous and inviscid Burgers equations. Traveling wave solutions are found for a general class of filters and are shown to converge to weak solutions of the inviscid Burgers equation with the correct wave speed. Numerical simulations are conducted in 1D and 2D cases where the shock behavior, shock thickness and kinetic energy decay are examined. Energy spectra are also examined and are shown to be related to the smoothness of the solutions. This approach is presented with the hope of being extended to shock regularization of compressible Euler equations

  17. New exact solutions to MKDV-Burgers equation and (2 + 1)-dimensional dispersive long wave equation via extended Riccati equation method

    International Nuclear Information System (INIS)

    Kong Cuicui; Wang Dan; Song Lina; Zhang Hongqing

    2009-01-01

    In this paper, with the aid of symbolic computation and a general ansaetz, we presented a new extended rational expansion method to construct new rational formal exact solutions to nonlinear partial differential equations. In order to illustrate the effectiveness of this method, we apply it to the MKDV-Burgers equation and the (2 + 1)-dimensional dispersive long wave equation, then several new kinds of exact solutions are successfully obtained by using the new ansaetz. The method can also be applied to other nonlinear partial differential equations.

  18. TRAVELING WAVE SOLUTIONS OF SOME FRACTIONAL DIFFERENTIAL EQUATIONS

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    SERIFE MUGE EGE

    2016-07-01

    Full Text Available The modified Kudryashov method is powerful, efficient and can be used as an alternative to establish new solutions of different type of fractional differential equations applied in mathematical physics. In this article, we’ve constructed new traveling wave solutions including symmetrical Fibonacci function solutions, hyperbolic function solutions and rational solutions of the space-time fractional Cahn Hillihard equation D_t^α u − γD_x^α u − 6u(D_x^α u^2 − (3u^2 − 1D_x^α (D_x^α u + D_x^α(D_x^α(D_x^α(D_x^α u = 0 and the space-time fractional symmetric regularized long wave (SRLW equation D_t^α(D_t^α u + D_x^α(D_x^α u + uD_t^α(D_x^α u + D_x^α u D_t^α u + D_t^α(D_t^α(D_x^α(D_x^α u = 0 via modified Kudryashov method. In addition, some of the solutions are described in the figures with the help of Mathematica.

  19. Traveling wave solutions to some nonlinear fractional partial differential equations through the rational (G′/G-expansion method

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    Tarikul Islam

    2018-03-01

    Full Text Available In this article, the analytical solutions to the space-time fractional foam drainage equation and the space-time fractional symmetric regularized long wave (SRLW equation are successfully examined by the recently established rational (G′/G-expansion method. The suggested equations are reduced into the nonlinear ordinary differential equations with the aid of the fractional complex transform. Consequently, the theories of the ordinary differential equations are implemented effectively. Three types closed form traveling wave solutions, such as hyperbolic function, trigonometric function and rational, are constructed by using the suggested method in the sense of conformable fractional derivative. The obtained solutions might be significant to analyze the depth and spacing of parallel subsurface drain and small-amplitude long wave on the surface of the water in a channel. It is observed that the performance of the rational (G′/G-expansion method is reliable and will be used to establish new general closed form solutions for any other NPDEs of fractional order.

  20. The collision of multimode dromions and a firewall in the two-component long-wave-short-wave resonance interaction equation

    International Nuclear Information System (INIS)

    Radha, R; Kumar, C Senthil; Lakshmanan, M; Gilson, C R

    2009-01-01

    In this communication, we investigate the two-component long-wave-short-wave resonance interaction equation and show that it admits the Painleve property. We then suitably exploit the recently developed truncated Painleve approach to generate exponentially localized solutions for the short-wave components S (1) and S (2) while the long wave L admits a line soliton only. The exponentially localized solutions driving the short waves S (1) and S (2) in the y-direction are endowed with different energies (intensities) and are called 'multimode dromions'. We also observe that the multimode dromions suffer from intramodal inelastic collision while the existence of a firewall across the modes prevents the switching of energy between the modes. (fast track communication)

  1. Wave-equation Qs Inversion of Skeletonized Surface Waves

    KAUST Repository

    Li, Jing

    2017-02-08

    We present a skeletonized inversion method that inverts surface-wave data for the Qs quality factor. Similar to the inversion of dispersion curves for the S-wave velocity model, the complicated surface-wave arrivals are skeletonized as simpler data, namely the amplitude spectra of the windowed Rayleigh-wave arrivals. The optimal Qs model is the one that minimizes the difference in the peak frequencies of the predicted and observed Rayleigh wave arrivals using a gradient-based wave-equation optimization method. Solutions to the viscoelastic wave-equation are used to compute the predicted Rayleigh-wave arrivals and the misfit gradient at every iteration. This procedure, denoted as wave-equation Qs inversion (WQs), does not require the assumption of a layered model and tends to have fast and robust convergence compared to full waveform inversion (FWI). Numerical examples with synthetic and field data demonstrate that the WQs method can accurately invert for a smoothed approximation to the subsurface Qs distribution as long as the Vs model is known with sufficient accuracy.

  2. Skeletonized wave-equation Qs tomography using surface waves

    KAUST Repository

    Li, Jing

    2017-08-17

    We present a skeletonized inversion method that inverts surface-wave data for the Qs quality factor. Similar to the inversion of dispersion curves for the S-wave velocity model, the complicated surface-wave arrivals are skeletonized as simpler data, namely the amplitude spectra of the windowed Rayleigh-wave arrivals. The optimal Qs model is then found that minimizes the difference in the peak frequencies of the predicted and observed Rayleigh wave arrivals using a gradient-based wave-equation optimization method. Solutions to the viscoelastic wave-equation are used to compute the predicted Rayleigh-wave arrivals and the misfit gradient at every iteration. This procedure, denoted as wave-equation Qs tomography (WQs), does not require the assumption of a layered model and tends to have fast and robust convergence compared to Q full waveform inversion (Q-FWI). Numerical examples with synthetic and field data demonstrate that the WQs method can accurately invert for a smoothed approximation to the subsur-face Qs distribution as long as the Vs model is known with sufficient accuracy.

  3. Wave-equation Qs Inversion of Skeletonized Surface Waves

    KAUST Repository

    Li, Jing; Dutta, Gaurav; Schuster, Gerard T.

    2017-01-01

    We present a skeletonized inversion method that inverts surface-wave data for the Qs quality factor. Similar to the inversion of dispersion curves for the S-wave velocity model, the complicated surface-wave arrivals are skeletonized as simpler data, namely the amplitude spectra of the windowed Rayleigh-wave arrivals. The optimal Qs model is the one that minimizes the difference in the peak frequencies of the predicted and observed Rayleigh wave arrivals using a gradient-based wave-equation optimization method. Solutions to the viscoelastic wave-equation are used to compute the predicted Rayleigh-wave arrivals and the misfit gradient at every iteration. This procedure, denoted as wave-equation Qs inversion (WQs), does not require the assumption of a layered model and tends to have fast and robust convergence compared to full waveform inversion (FWI). Numerical examples with synthetic and field data demonstrate that the WQs method can accurately invert for a smoothed approximation to the subsurface Qs distribution as long as the Vs model is known with sufficient accuracy.

  4. On the Stochastic Wave Equation with Nonlinear Damping

    International Nuclear Information System (INIS)

    Kim, Jong Uhn

    2008-01-01

    We discuss an initial boundary value problem for the stochastic wave equation with nonlinear damping. We establish the existence and uniqueness of a solution. Our method for the existence of pathwise solutions consists of regularization of the equation and data, the Galerkin approximation and an elementary measure-theoretic argument. We also prove the existence of an invariant measure when the equation has pure nonlinear damping

  5. Rogue periodic waves of the modified KdV equation

    Science.gov (United States)

    Chen, Jinbing; Pelinovsky, Dmitry E.

    2018-05-01

    Rogue periodic waves stand for rogue waves on a periodic background. Two families of travelling periodic waves of the modified Korteweg–de Vries (mKdV) equation in the focusing case are expressed by the Jacobian elliptic functions dn and cn. By using one-fold and two-fold Darboux transformations of the travelling periodic waves, we construct new explicit solutions for the mKdV equation. Since the dn-periodic wave is modulationally stable with respect to long-wave perturbations, the new solution constructed from the dn-periodic wave is a nonlinear superposition of an algebraically decaying soliton and the dn-periodic wave. On the other hand, since the cn-periodic wave is modulationally unstable with respect to long-wave perturbations, the new solution constructed from the cn-periodic wave is a rogue wave on the cn-periodic background, which generalizes the classical rogue wave (the so-called Peregrine’s breather) of the nonlinear Schrödinger equation. We compute the magnification factor for the rogue cn-periodic wave of the mKdV equation and show that it remains constant for all amplitudes. As a by-product of our work, we find explicit expressions for the periodic eigenfunctions of the spectral problem associated with the dn and cn periodic waves of the mKdV equation.

  6. Traveling waves and conservation laws for highly nonlinear wave equations modeling Hertz chains

    Science.gov (United States)

    Przedborski, Michelle; Anco, Stephen C.

    2017-09-01

    A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, homogeneous, discrete chains with a general power-law contact interaction is studied. For this wave equation, all solitary wave solutions and all nonlinear periodic wave solutions, along with all conservation laws, are derived. The solutions are explicitly parameterized in terms of the asymptotic value of the wave amplitude in the case of solitary waves and the peak of the wave amplitude in the case of nonlinear periodic waves. All cases in which the solution expressions can be stated in an explicit analytic form using elementary functions are worked out. In these cases, explicit expressions for the total energy and total momentum for all solutions are obtained as well. The derivation of the solutions uses the conservation laws combined with an energy analysis argument to reduce the wave equation directly to a separable first-order differential equation that determines the wave amplitude in terms of the traveling wave variable. This method can be applied more generally to other highly nonlinear wave equations.

  7. Soliton solution for nonlinear partial differential equations by cosine-function method

    International Nuclear Information System (INIS)

    Ali, A.H.A.; Soliman, A.A.; Raslan, K.R.

    2007-01-01

    In this Letter, we established a traveling wave solution by using Cosine-function algorithm for nonlinear partial differential equations. The method is used to obtain the exact solutions for five different types of nonlinear partial differential equations such as, general equal width wave equation (GEWE), general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKdV), general improved Korteweg-de Vries equation (GIKdV), and Coupled equal width wave equations (CEWE), which are the important soliton equations

  8. The investigation for (2+1)-dimensional Eckhaus-type extension of the dispersive long wave equation

    International Nuclear Information System (INIS)

    Yan Zhenya

    2004-01-01

    The (2+1)-dimensional Eckhaus-type extension of the dispersive long wave (EEDLW) equation is investigated, which was obtained in the appropriate approximation from the basic equations of hydrodynamics. Though it has no Painleve property, we gain an auto-Baecklund transformation (aBT) by truncating the Laurent series expansion at O(w 0 ). In particular, the special one of the aBT establishes a relationship between the EEDLW equation and a set of three linear partial differential equations involving the well-known heat equation. Finally many types of new exact solutions of the EEDLW equation are found from the obtained aBT and some proper ansaetze, which may be useful to explain some physical phenomena

  9. Wave dynamics of regular and chaotic rays

    International Nuclear Information System (INIS)

    McDonald, S.W.

    1983-09-01

    In order to investigate general relationships between waves and rays in chaotic systems, I study the eigenfunctions and spectrum of a simple model, the two-dimensional Helmholtz equation in a stadium boundary, for which the rays are ergodic. Statistical measurements are performed so that the apparent randomness of the stadium modes can be quantitatively contrasted with the familiar regularities observed for the modes in a circular boundary (with integrable rays). The local spatial autocorrelation of the eigenfunctions is constructed in order to indirectly test theoretical predictions for the nature of the Wigner distribution corresponding to chaotic waves. A portion of the large-eigenvalue spectrum is computed and reported in an appendix; the probability distribution of successive level spacings is analyzed and compared with theoretical predictions. The two principal conclusions are: 1) waves associated with chaotic rays may exhibit randomly situated localized regions of high intensity; 2) the Wigner function for these waves may depart significantly from being uniformly distributed over the surface of constant frequency in the ray phase space

  10. Finite-dimensional attractor for a composite system of wave/plate equations with localized damping

    International Nuclear Information System (INIS)

    Bucci, Francesca; Toundykov, Daniel

    2010-01-01

    The long-term behaviour of solutions to a model for acoustic–structure interactions is addressed; the system consists of coupled semilinear wave (3D) and plate equations with nonlinear damping and critical sources. The questions of interest are the existence of a global attractor for the dynamics generated by this composite system as well as dimensionality and regularity of the attractor. A distinct and challenging feature of the problem is the geometrically restricted dissipation on the wave component of the system. It is shown that the existence of a global attractor of finite fractal dimension—established in a previous work by Bucci et al (2007 Commun. Pure Appl. Anal. 6 113–40) only in the presence of full-interior acoustic damping—holds even in the case of localized dissipation. This nontrivial generalization is inspired by, and consistent with, the recent advances in the study of wave equations with nonlinear localized damping

  11. Soliton solutions to the fifth-order Korteweg-de Vries equation and their applications to surface and internal water waves

    Science.gov (United States)

    Khusnutdinova, K. R.; Stepanyants, Y. A.; Tranter, M. R.

    2018-02-01

    We study solitary wave solutions of the fifth-order Korteweg-de Vries equation which contains, besides the traditional quadratic nonlinearity and third-order dispersion, additional terms including cubic nonlinearity and fifth order linear dispersion, as well as two nonlinear dispersive terms. An exact solitary wave solution to this equation is derived, and the dependence of its amplitude, width, and speed on the parameters of the governing equation is studied. It is shown that the derived solution can represent either an embedded or regular soliton depending on the equation parameters. The nonlinear dispersive terms can drastically influence the existence of solitary waves, their nature (regular or embedded), profile, polarity, and stability with respect to small perturbations. We show, in particular, that in some cases embedded solitons can be stable even with respect to interactions with regular solitons. The results obtained are applicable to surface and internal waves in fluids, as well as to waves in other media (plasma, solid waveguides, elastic media with microstructure, etc.).

  12. Regularity criteria for incompressible magnetohydrodynamics equations in three dimensions

    International Nuclear Information System (INIS)

    Lin, Hongxia; Du, Lili

    2013-01-01

    In this paper, we give some new global regularity criteria for three-dimensional incompressible magnetohydrodynamics (MHD) equations. More precisely, we provide some sufficient conditions in terms of the derivatives of the velocity or pressure, for the global regularity of strong solutions to 3D incompressible MHD equations in the whole space, as well as for periodic boundary conditions. Moreover, the regularity criterion involving three of the nine components of the velocity gradient tensor is also obtained. The main results generalize the recent work by Cao and Wu (2010 Two regularity criteria for the 3D MHD equations J. Diff. Eqns 248 2263–74) and the analysis in part is based on the works by Cao C and Titi E (2008 Regularity criteria for the three-dimensional Navier–Stokes equations Indiana Univ. Math. J. 57 2643–61; 2011 Gobal regularity criterion for the 3D Navier–Stokes equations involving one entry of the velocity gradient tensor Arch. Rational Mech. Anal. 202 919–32) for 3D incompressible Navier–Stokes equations. (paper)

  13. Regularity of difference equations on Banach spaces

    CERN Document Server

    Agarwal, Ravi P; Lizama, Carlos

    2014-01-01

    This work introduces readers to the topic of maximal regularity for difference equations. The authors systematically present the method of maximal regularity, outlining basic linear difference equations along with relevant results. They address recent advances in the field, as well as basic semigroup and cosine operator theories in the discrete setting. The authors also identify some open problems that readers may wish to take up for further research. This book is intended for graduate students and researchers in the area of difference equations, particularly those with advance knowledge of and interest in functional analysis.

  14. True amplitude wave equation migration arising from true amplitude one-way wave equations

    Science.gov (United States)

    Zhang, Yu; Zhang, Guanquan; Bleistein, Norman

    2003-10-01

    One-way wave operators are powerful tools for use in forward modelling and inversion. Their implementation, however, involves introduction of the square root of an operator as a pseudo-differential operator. Furthermore, a simple factoring of the wave operator produces one-way wave equations that yield the same travel times as the full wave equation, but do not yield accurate amplitudes except for homogeneous media and for almost all points in heterogeneous media. Here, we present augmented one-way wave equations. We show that these equations yield solutions for which the leading order asymptotic amplitude as well as the travel time satisfy the same differential equations as the corresponding functions for the full wave equation. Exact representations of the square-root operator appearing in these differential equations are elusive, except in cases in which the heterogeneity of the medium is independent of the transverse spatial variables. Here, we address the fully heterogeneous case. Singling out depth as the preferred direction of propagation, we introduce a representation of the square-root operator as an integral in which a rational function of the transverse Laplacian appears in the integrand. This allows us to carry out explicit asymptotic analysis of the resulting one-way wave equations. To do this, we introduce an auxiliary function that satisfies a lower dimensional wave equation in transverse spatial variables only. We prove that ray theory for these one-way wave equations leads to one-way eikonal equations and the correct leading order transport equation for the full wave equation. We then introduce appropriate boundary conditions at z = 0 to generate waves at depth whose quotient leads to a reflector map and an estimate of the ray theoretical reflection coefficient on the reflector. Thus, these true amplitude one-way wave equations lead to a 'true amplitude wave equation migration' (WEM) method. In fact, we prove that applying the WEM imaging condition

  15. On Long-Time Instabilities in Staggered Finite Difference Simulations of the Seismic Acoustic Wave Equations on Discontinuous Grids

    KAUST Repository

    Gao, Longfei; Ketcheson, David I.; Keyes, David E.

    2017-01-01

    We consider the long-time instability issue associated with finite difference simulation of seismic acoustic wave equations on discontinuous grids. This issue is exhibited by a prototype algebraic problem abstracted from practical application

  16. Persistence of travelling waves in a generalized Fisher equation

    International Nuclear Information System (INIS)

    Kyrychko, Yuliya N.; Blyuss, Konstantin B.

    2009-01-01

    Travelling waves of the Fisher equation with arbitrary power of nonlinearity are studied in the presence of long-range diffusion. Using analogy between travelling waves and heteroclinic solutions of corresponding ODEs, we employ the geometric singular perturbation theory to prove the persistence of these waves when the influence of long-range effects is small. When the long-range diffusion coefficient becomes larger, the behaviour of travelling waves can only be studied numerically. In this case we find that starting with some values, solutions of the model lose monotonicity and become oscillatory

  17. Theoretical analysis and experimental study of oxygen transfer under regular and non-breaking waves

    Institute of Scientific and Technical Information of China (English)

    尹则高; 梁丙臣; 王乐

    2013-01-01

    The dissolved oxygen concentration is an important index of water quality, and the atmosphere is one of the important sources of the dissolved oxygen. In this paper, the mass conservation law and the dimensional analysis method are employed to study the oxygen transfer under regular and non-breaking waves, and a unified oxygen transfer coefficient equation is obtained with consi-deration of the effect of kinetic energy and wave period. An oxygen transfer experiment for the intermediate depth water wave is per-formed to measure the wave parameters and the dissolved oxygen concentration. The experimental data and the least squares method are used to determine the constant in the oxygen transfer coefficient equation. The experimental data and the previous reported data are also used to further validate the oxygen transfer coefficient, and the agreement is satisfactory. The unified equation shows that the oxygen transfer coefficient increases with the increase of a parameter coupled with the wave height and the wave length, but it de-creases with the increase of the wave period, which has a much greater influence on the oxygen transfer coefficient than the coupled parameter.

  18. A nonlinear wave equation in nonadiabatic flame propagation

    International Nuclear Information System (INIS)

    Booty, M.R.; Matalon, M.; Matkowsky, B.J.

    1988-01-01

    The authors derive a nonlinear wave equation from the diffusional thermal model of gaseous combustion to describe the evolution of a flame front. The equation arises as a long wave theory, for values of the volumeric heat loss in a neighborhood of the extinction point (beyond which planar uniformly propagating flames cease to exist), and for Lewis numbers near the critical value beyond which uniformly propagating planar flames lose stability via a degenerate Hopf bifurcation. Analysis of the equation suggests the possibility of a singularity developing in finite time

  19. Nonlocal symmetries, solitary waves and cnoidal periodic waves of the (2+1)-dimensional breaking soliton equation

    Science.gov (United States)

    Zou, Li; Tian, Shou-Fu; Feng, Lian-Li

    2017-12-01

    In this paper, we consider the (2+1)-dimensional breaking soliton equation, which describes the interaction of a Riemann wave propagating along the y-axis with a long wave along the x-axis. By virtue of the truncated Painlevé expansion method, we obtain the nonlocal symmetry, Bäcklund transformation and Schwarzian form of the equation. Furthermore, by using the consistent Riccati expansion (CRE), we prove that the breaking soliton equation is solvable. Based on the consistent tan-function expansion, we explicitly derive the interaction solutions between solitary waves and cnoidal periodic waves.

  20. Poincare group and relativistic wave equations in 2+1 dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Gitman, Dmitri M. [Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo, SP (Brazil); Shelepin, A.L. [Moscow Institute of Radio Engenering, Electronics and Automation, Moscow (Russian Federation)

    1997-09-07

    Using the generalized regular representation, an explicit construction of the unitary irreducible representations of the (2+1)-Poincare group is presented. A detailed description of the angular momentum and spin in 2+1 dimensions is given. On this base the relativistic wave equations for all spins (including fractional) are constructed. (author)

  1. Wave Equation Inversion of Skeletonized SurfaceWaves

    KAUST Repository

    Zhang, Zhendong

    2015-08-19

    We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh dispersion curve for the fundamental-mode. We call this wave equation inversion of skeletonized surface waves because the dispersion curve for the fundamental-mode Rayleigh wave is inverted using finite-difference solutions to the wave equation. The best match between the predicted and observed dispersion curves provides the optimal S-wave velocity model. Results with synthetic and field data illustrate the benefits and limitations of this method.

  2. Numerical study of the Kadomtsev-Petviashvili equation and dispersive shock waves

    Science.gov (United States)

    Grava, T.; Klein, C.; Pitton, G.

    2018-02-01

    A detailed numerical study of the long time behaviour of dispersive shock waves in solutions to the Kadomtsev-Petviashvili (KP) I equation is presented. It is shown that modulated lump solutions emerge from the dispersive shock waves. For the description of dispersive shock waves, Whitham modulation equations for KP are obtained. It is shown that the modulation equations near the soliton line are hyperbolic for the KPII equation while they are elliptic for the KPI equation leading to a focusing effect and the formation of lumps. Such a behaviour is similar to the appearance of breathers for the focusing nonlinear Schrödinger equation in the semiclassical limit.

  3. Wave-equation dispersion inversion

    KAUST Repository

    Li, Jing

    2016-12-08

    We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained from Rayleigh waves recorded by vertical-component geophones. Similar to wave-equation traveltime tomography, the complicated surface wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the phase-velocity and frequency domains. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2-D or 3-D S-wave velocity models. This procedure, denoted as wave-equation dispersion inversion (WD), does not require the assumption of a layered model and is significantly less prone to the cycle-skipping problems of full waveform inversion. The synthetic and field data examples demonstrate that WD can approximately reconstruct the S-wave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic data and the inversion of dispersion curves associated with Love waves.

  4. Analysis and computation of the elastic wave equation with random coefficients

    KAUST Repository

    Motamed, Mohammad

    2015-10-21

    We consider the stochastic initial-boundary value problem for the elastic wave equation with random coefficients and deterministic data. We propose a stochastic collocation method for computing statistical moments of the solution or statistics of some given quantities of interest. We study the convergence rate of the error in the stochastic collocation method. In particular, we show that, the rate of convergence depends on the regularity of the solution or the quantity of interest in the stochastic space, which is in turn related to the regularity of the deterministic data in the physical space and the type of the quantity of interest. We demonstrate that a fast rate of convergence is possible in two cases: for the elastic wave solutions with high regular data; and for some high regular quantities of interest even in the presence of low regular data. We perform numerical examples, including a simplified earthquake, which confirm the analysis and show that the collocation method is a valid alternative to the more traditional Monte Carlo sampling method for approximating quantities with high stochastic regularity.

  5. An extended Jacobi elliptic function rational expansion method and its application to (2+1)-dimensional dispersive long wave equation

    International Nuclear Information System (INIS)

    Wang Qi; Chen Yong; Zhang Hongqing

    2005-01-01

    With the aid of computerized symbolic computation, a new elliptic function rational expansion method is presented by means of a new general ansatz, in which periodic solutions of nonlinear partial differential equations that can be expressed as a finite Laurent series of some of 12 Jacobi elliptic functions, is more powerful than exiting Jacobi elliptic function methods and is very powerful to uniformly construct more new exact periodic solutions in terms of rational formal Jacobi elliptic function solution of nonlinear partial differential equations. As an application of the method, we choose a (2+1)-dimensional dispersive long wave equation to illustrate the method. As a result, we can successfully obtain the solutions found by most existing Jacobi elliptic function methods and find other new and more general solutions at the same time. Of course, more shock wave solutions or solitary wave solutions can be gotten at their limit condition

  6. An oscillating wave energy converter with nonlinear snap-through Power-Take-Off systems in regular waves

    Science.gov (United States)

    Zhang, Xian-tao; Yang, Jian-min; Xiao, Long-fei

    2016-07-01

    Floating oscillating bodies constitute a large class of wave energy converters, especially for offshore deployment. Usually the Power-Take-Off (PTO) system is a directly linear electric generator or a hydraulic motor that drives an electric generator. The PTO system is simplified as a linear spring and a linear damper. However the conversion is less powerful with wave periods off resonance. Thus, a nonlinear snap-through mechanism with two symmetrically oblique springs and a linear damper is applied in the PTO system. The nonlinear snap-through mechanism is characteristics of negative stiffness and double-well potential. An important nonlinear parameter γ is defined as the ratio of half of the horizontal distance between the two springs to the original length of both springs. Time domain method is applied to the dynamics of wave energy converter in regular waves. And the state space model is used to replace the convolution terms in the time domain equation. The results show that the energy harvested by the nonlinear PTO system is larger than that by linear system for low frequency input. While the power captured by nonlinear converters is slightly smaller than that by linear converters for high frequency input. The wave amplitude, damping coefficient of PTO systems and the nonlinear parameter γ affect power capture performance of nonlinear converters. The oscillation of nonlinear wave energy converters may be local or periodically inter well for certain values of the incident wave frequency and the nonlinear parameter γ, which is different from linear converters characteristics of sinusoidal response in regular waves.

  7. Analysis of regularized Navier-Stokes equations, 2

    Science.gov (United States)

    Ou, Yuh-Roung; Sritharan, S. S.

    1989-01-01

    A practically important regularization of the Navier-Stokes equations was analyzed. As a continuation of the previous work, the structure of the attractors characterizing the solutins was studied. Local as well as global invariant manifolds were found. Regularity properties of these manifolds are analyzed.

  8. The behaviour of hydrogen-like atoms in an intense long-wave field

    International Nuclear Information System (INIS)

    Brodsky, A.M.

    1979-01-01

    The equations, which permit the calculation by means of regular operations of multiphoton photoionisation cross sections and the dynamic polarisabilities in an intense classical long-wave electromagnetic field, are considered for a hydrogen atom. The calculations have been performed for a circularly polarised field. A quantitative expression has been derived for the Lamb shift analogue, which can be verified experimentally. Within the framework of the problem the interaction at small distances is self-compensated and reduced to a constant potential. This conclusion is of general interest for the theory of strong interactions. (author)

  9. Numerical analysis of regular waves over an onshore oscillating water column

    Energy Technology Data Exchange (ETDEWEB)

    Davyt, D.P.; Teixeira, P.R.F. [Universidade Federal do Rio Grande (FURG), RS (Brazil)], E-mail: pauloteixeira@furg.br; Ramalhais, R. [Universidade Nova de Lisboa, Caparica (Portugal). Fac. de Ciencias e Tecnologia; Didier, E. [Laboratorio Nacional de Engenharia Civil, Lisboa (Portugal)], E-mail: edidier@lnec.pt

    2010-07-01

    The potential of wave energy along coastal areas is a particularly attractive option in regions of high latitude, such as the coasts of northern Europe, North America, New Zealand, Chile and Argentina where high densities of annual average wave energy are found (typically between 40 and 100 kW/m of wave front). Power estimated in the south of Brazil is 30kW/m, creating a possible alternative of source energy in the region. There are many types and designs of equipment to capture energy from waves under analysis, such as the oscillating water column type (OWC) which has been one of the first to be developed and installed at sea. Despite being one of the most analyzed wave energy converter devices, there are few case studies using numerical simulation. In this context, the numerical analysis of regular waves over an onshore OWC is the main objective of this paper. The numerical models FLUINCO and FLUENT are used for achieving this goal. The FLUINCO model is based on RANS equations which are discretized using the two-step semi-implicit Taylor-Galerkin method. An arbitrary Lagrangian Eulerian formulation is used to enable the solution of problems involving free surface movements. The FLUENT code (version 6.3.26) is based on the finite volume method to solve RANS equations. Volume of Fluid method (VOF) is used for modeling free surface flows. Time integration is achieved by a second order implicit scheme, momentum equations are discretized using MUSCL scheme and HRIC (High Resolution Interface Capturing) scheme is used for convective term of VOF transport equation. The case study consists of a 10.m deep channel with a 10 m wide chamber at its end. One meter high waves with different periods are simulated. Comparisons between FLUINCO and FLUENT results are presented. Free surface elevation inside the chamber; velocity distribution and streamlines; amplification factor (relation between wave height inside the chamber and incident wave height); phase angle (angular

  10. Skeletonized wave equation of surface wave dispersion inversion

    KAUST Repository

    Li, Jing

    2016-09-06

    We present the theory for wave equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. Similar to wave-equation travel-time inversion, the complicated surface-wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the (kx,ω) domain. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2D or 3D velocity models. This procedure, denoted as wave equation dispersion inversion (WD), does not require the assumption of a layered model and is less prone to the cycle skipping problems of full waveform inversion (FWI). The synthetic and field data examples demonstrate that WD can accurately reconstruct the S-wave velocity distribution in laterally heterogeneous media.

  11. Regularized plane-wave least-squares Kirchhoff migration

    KAUST Repository

    Wang, Xin

    2013-09-22

    A Kirchhoff least-squares migration (LSM) is developed in the prestack plane-wave domain to increase the quality of migration images. A regularization term is included that accounts for mispositioning of reflectors due to errors in the velocity model. Both synthetic and field results show that: 1) LSM with a reflectivity model common for all the plane-wave gathers provides the best image when the migration velocity model is accurate, but it is more sensitive to the velocity errors, 2) the regularized plane-wave LSM is more robust in the presence of velocity errors, and 3) LSM achieves both computational and IO saving by plane-wave encoding compared to shot-domain LSM for the models tested.

  12. Exact Solutions of the Space Time Fractional Symmetric Regularized Long Wave Equation Using Different Methods

    Directory of Open Access Journals (Sweden)

    Özkan Güner

    2014-01-01

    Full Text Available We apply the functional variable method, exp-function method, and (G′/G-expansion method to establish the exact solutions of the nonlinear fractional partial differential equation (NLFPDE in the sense of the modified Riemann-Liouville derivative. As a result, some new exact solutions for them are obtained. The results show that these methods are very effective and powerful mathematical tools for solving nonlinear fractional equations arising in mathematical physics. As a result, these methods can also be applied to other nonlinear fractional differential equations.

  13. Linear fractional diffusion-wave equation for scientists and engineers

    CERN Document Server

    Povstenko, Yuriy

    2015-01-01

    This book systematically presents solutions to the linear time-fractional diffusion-wave equation. It introduces the integral transform technique and discusses the properties of the Mittag-Leffler, Wright, and Mainardi functions that appear in the solutions. The time-nonlocal dependence between the flux and the gradient of the transported quantity with the “long-tail” power kernel results in the time-fractional diffusion-wave equation with the Caputo fractional derivative. Time-nonlocal generalizations of classical Fourier’s, Fick’s and Darcy’s laws are considered and different kinds of boundary conditions for this equation are discussed (Dirichlet, Neumann, Robin, perfect contact). The book provides solutions to the fractional diffusion-wave equation with one, two and three space variables in Cartesian, cylindrical and spherical coordinates. The respective sections of the book can be used for university courses on fractional calculus, heat and mass transfer, transport processes in porous media and ...

  14. Tur\\'an type inequalities for regular Coulomb wave functions

    OpenAIRE

    Baricz, Árpád

    2015-01-01

    Tur\\'an, Mitrinovi\\'c-Adamovi\\'c and Wilker type inequalities are deduced for regular Coulomb wave functions. The proofs are based on a Mittag-Leffler expansion for the regular Coulomb wave function, which may be of independent interest. Moreover, some complete monotonicity results concerning the Coulomb zeta functions and some interlacing properties of the zeros of Coulomb wave functions are given.

  15. Wave Equation Inversion of Skeletonized SurfaceWaves

    KAUST Repository

    Zhang, Zhendong; Liu, Yike; Schuster, Gerard T.

    2015-01-01

    We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh dispersion curve for the fundamental-mode. We call this wave equation inversion of skeletonized surface waves because the dispersion curve

  16. Skeletonized wave equation of surface wave dispersion inversion

    KAUST Repository

    Li, Jing; Schuster, Gerard T.

    2016-01-01

    We present the theory for wave equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. Similar to wave-equation travel

  17. Linear superposition solutions to nonlinear wave equations

    International Nuclear Information System (INIS)

    Liu Yu

    2012-01-01

    The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic, triangle, and exponential functions, and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics. The linear superposition solutions to the generalized KdV equation K(2,2,1), the Oliver water wave equation, and the k(n, n) equation are given. The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed, and the reason why the solutions with the forms of hyperbolic, triangle, and exponential functions can form the linear superposition solutions is also discussed

  18. Ultra Deep Wave Equation Imaging and Illumination

    Energy Technology Data Exchange (ETDEWEB)

    Alexander M. Popovici; Sergey Fomel; Paul Sava; Sean Crawley; Yining Li; Cristian Lupascu

    2006-09-30

    In this project we developed and tested a novel technology, designed to enhance seismic resolution and imaging of ultra-deep complex geologic structures by using state-of-the-art wave-equation depth migration and wave-equation velocity model building technology for deeper data penetration and recovery, steeper dip and ultra-deep structure imaging, accurate velocity estimation for imaging and pore pressure prediction and accurate illumination and amplitude processing for extending the AVO prediction window. Ultra-deep wave-equation imaging provides greater resolution and accuracy under complex geologic structures where energy multipathing occurs, than what can be accomplished today with standard imaging technology. The objective of the research effort was to examine the feasibility of imaging ultra-deep structures onshore and offshore, by using (1) wave-equation migration, (2) angle-gathers velocity model building, and (3) wave-equation illumination and amplitude compensation. The effort consisted of answering critical technical questions that determine the feasibility of the proposed methodology, testing the theory on synthetic data, and finally applying the technology for imaging ultra-deep real data. Some of the questions answered by this research addressed: (1) the handling of true amplitudes in the downward continuation and imaging algorithm and the preservation of the amplitude with offset or amplitude with angle information required for AVO studies, (2) the effect of several imaging conditions on amplitudes, (3) non-elastic attenuation and approaches for recovering the amplitude and frequency, (4) the effect of aperture and illumination on imaging steep dips and on discriminating the velocities in the ultra-deep structures. All these effects were incorporated in the final imaging step of a real data set acquired specifically to address ultra-deep imaging issues, with large offsets (12,500 m) and long recording time (20 s).

  19. The relativistic electron wave equation

    International Nuclear Information System (INIS)

    Dirac, P.A.M.

    1977-08-01

    The paper was presented at the European Conference on Particle Physics held in Budapest between the 4th and 9th July of 1977. A short review is given on the birth of the relativistic electron wave equation. After Schroedinger has shown the equivalence of his wave mechanics and the matrix mechanics of Heisenberg, a general transformation theory was developed by the author. This theory required a relativistic wave equation linear in delta/delta t. As the Klein--Gordon equation available at this time did not satisfy this condition the development of a new equation became necessary. The equation which was found gave the value of the electron spin and magnetic moment automatically. (D.P.)

  20. Analysis of wave equation in electromagnetic field by Proca equation

    International Nuclear Information System (INIS)

    Pamungkas, Oky Rio; Soeparmi; Cari

    2017-01-01

    This research is aimed to analyze wave equation for the electric and magnetic field, vector and scalar potential, and continuity equation using Proca equation. Then, also analyze comparison of the solution on Maxwell and Proca equation for scalar potential and electric field, both as a function of distance and constant wave number. (paper)

  1. Nonlinear wave equation with intrinsic wave particle dualism

    International Nuclear Information System (INIS)

    Klein, J.J.

    1976-01-01

    A nonlinear wave equation derived from the sine-Gordon equation is shown to possess a variety of solutions, the most interesting of which is a solution that describes a wave packet travelling with velocity usub(e) modulating a carrier wave travelling with velocity usub(c). The envelop and carrier wave speeds agree precisely with the group and phase velocities found by de Broglie for matter waves. No spreading is exhibited by the soliton, so that it behaves exactly like a particle in classical mechanics. Moreover, the classically computed energy E of the disturbance turns out to be exactly equal to the frequency ω of the carrier wave, so that the Planck relation is automatically satisfied without postulating a particle-wave dualism. (author)

  2. Prediction of regular wave loads on a fixed offshore oscillating water column-wave energy converter using CFD

    Directory of Open Access Journals (Sweden)

    Ahmed Elhanafi

    2016-12-01

    Full Text Available In this paper, hydrodynamic wave loads on an offshore stationary–floating oscillating water column (OWC are investigated via a 2D and 3D computational fluid dynamics (CFD modeling based on the RANS equations and the VOF surface capturing scheme. The CFD model is validated against previous experiments for nonlinear regular wave interactions with a surface-piercing stationary barge. Following the validation stage, the numerical model is modified to consider the pneumatic damping effect, and an extensive campaign of numerical tests is carried out to study the wave–OWC interactions for different wave periods, wave heights and pneumatic damping factors. It is found that the horizontal wave force is usually larger than the vertical one. Also, there a direct relationship between the pneumatic and hydrodynamic vertical forces with a maximum vertical force almost at the device natural frequency, whereas the pneumatic damping has a little effect on the horizontal force. Additionally, simulating the turbine damping with an orifice plate induces higher vertical loads than utilizing a slot opening. Furthermore, 3D modeling significantly escalates and declines the predicted hydrodynamic vertical and horizontal wave loads, respectively.

  3. Parsimonious wave-equation travel-time inversion for refraction waves

    KAUST Repository

    Fu, Lei

    2017-02-14

    We present a parsimonious wave-equation travel-time inversion technique for refraction waves. A dense virtual refraction dataset can be generated from just two reciprocal shot gathers for the sources at the endpoints of the survey line, with N geophones evenly deployed along the line. These two reciprocal shots contain approximately 2N refraction travel times, which can be spawned into O(N2) refraction travel times by an interferometric transformation. Then, these virtual refraction travel times are used with a source wavelet to create N virtual refraction shot gathers, which are the input data for wave-equation travel-time inversion. Numerical results show that the parsimonious wave-equation travel-time tomogram has about the same accuracy as the tomogram computed by standard wave-equation travel-time inversion. The most significant benefit is that a reciprocal survey is far less time consuming than the standard refraction survey where a source is excited at each geophone location.

  4. Dynamics and bifurcations of travelling wave solutions of R(m, n ...

    Indian Academy of Sciences (India)

    and de Vries [6] in 1895 showed the balance between the weak nonlinear term uux and the dispersion term ... family of regularized long-wave Boussinseq equations (R(m, n) equations in short) utt + a(un)xx + ...... This is our task in future work.

  5. A series of new soliton-like solutions and double-like periodic solutions of a (2 + 1)-dimensional dispersive long wave equation

    International Nuclear Information System (INIS)

    Yong Chen; Qi Wang

    2005-01-01

    In this paper, we extend the algebraic method proposed by Fan (Chaos, Solitons and Fractals 20 (2004) 609) and the improved extended tanh method by Yomba (Chaos, Solitons and Fractals 20 (2004) 1135) to uniformly construct a series of soliton-like solutions and double-like periodic solutions for nonlinear partial differential equations (NPDE). Some new soliton-like solutions and double-like periodic solutions of a (2 + 1)-dimensional dispersive long wave equation are obtained

  6. Nonlinear wave equations

    CERN Document Server

    Li, Tatsien

    2017-01-01

    This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.

  7. Asymptotic approach for the nonlinear equatorial long wave interactions

    International Nuclear Information System (INIS)

    Ramirez Gutierrez, Enver; Silva Dias, Pedro L; Raupp, Carlos

    2011-01-01

    In the present work we use an asymptotic approach to obtain the long wave equations. The shallow water equation is put as a function of an external parameter that is a measure of both the spatial scales anisotropy and the fast to slow time ratio. The values given to the external parameters are consistent with those computed using typical values of the perturbations in tropical dynamics. Asymptotically, the model converge toward the long wave model. Thus, it is possible to go toward the long wave approximation through intermediate realizable states. With this approach, the resonant nonlinear wave interactions are studied. To simplify, the reduced dynamics of a single resonant triad is used for some selected equatorial trios. It was verified by both theoretical and numerical results that the nonlinear energy exchange period increases smoothly as we move toward the long wave approach. The magnitude of the energy exchanges is also modified, but in this case depends on the particular triad used and also on the initial energy partition among the triad components. Some implications of the results for the tropical dynamics are discussed. In particular, we discuss the implications of the results for El Nino and the Madden-Julian in connection with other scales of time and spatial variability.

  8. Lipschitz Regularity of Solutions for Mixed Integro-Differential Equations

    OpenAIRE

    Barles, Guy; Chasseigne, Emmanuel; Ciomaga, Adina; Imbert, Cyril

    2011-01-01

    We establish new Hoelder and Lipschitz estimates for viscosity solutions of a large class of elliptic and parabolic nonlinear integro-differential equations, by the classical Ishii-Lions's method. We thus extend the Hoelder regularity results recently obtained by Barles, Chasseigne and Imbert (2011). In addition, we deal with a new class of nonlocal equations that we term mixed integro-differential equations. These equations are particularly interesting, as they are degenerate both in the loc...

  9. Conservative numerical methods for solitary wave interactions

    Energy Technology Data Exchange (ETDEWEB)

    Duran, A; Lopez-Marcos, M A [Departamento de Matematica Aplicada y Computacion, Facultad de Ciencias, Universidad de Valladolid, Paseo del Prado de la Magdalena s/n, 47005 Valladolid (Spain)

    2003-07-18

    The purpose of this paper is to show the advantages that represent the use of numerical methods that preserve invariant quantities in the study of solitary wave interactions for the regularized long wave equation. It is shown that the so-called conservative methods are more appropriate to study the phenomenon and provide a dynamic point of view that allows us to estimate the changes in the parameters of the solitary waves after the collision.

  10. Regularity of the Maxwell equations in heterogeneous media and Lipschitz domains

    KAUST Repository

    Bonito, Andrea

    2013-12-01

    This note establishes regularity estimates for the solution of the Maxwell equations in Lipschitz domains with non-smooth coefficients and minimal regularity assumptions. The argumentation relies on elliptic regularity estimates for the Poisson problem with non-smooth coefficients. © 2013 Elsevier Ltd.

  11. An Inverse Source Problem for a One-dimensional Wave Equation: An Observer-Based Approach

    KAUST Repository

    Asiri, Sharefa M.

    2013-05-25

    Observers are well known in the theory of dynamical systems. They are used to estimate the states of a system from some measurements. However, recently observers have also been developed to estimate some unknowns for systems governed by Partial differential equations. Our aim is to design an observer to solve inverse source problem for a one dimensional wave equation. Firstly, the problem is discretized in both space and time and then an adaptive observer based on partial field measurements (i.e measurements taken form the solution of the wave equation) is applied to estimate both the states and the source. We see the effectiveness of this observer in both noise-free and noisy cases. In each case, numerical simulations are provided to illustrate the effectiveness of this approach. Finally, we compare the performance of the observer approach with Tikhonov regularization approach.

  12. Spatial evolution equation of wind wave growth

    Institute of Scientific and Technical Information of China (English)

    WANG; Wei; (王; 伟); SUN; Fu; (孙; 孚); DAI; Dejun; (戴德君)

    2003-01-01

    Based on the dynamic essence of air-sea interactions, a feedback type of spatial evolution equation is suggested to match reasonably the growing process of wind waves. This simple equation involving the dominant factors of wind wave growth is able to explain the transfer of energy from high to low frequencies without introducing the concept of nonlinear wave-wave interactions, and the results agree well with observations. The rate of wave height growth derived in this dissertation is applicable to both laboratory and open sea, which solidifies the physical basis of using laboratory experiments to investigate the generation of wind waves. Thus the proposed spatial evolution equation provides a new approach for the research on dynamic mechanism of air-sea interactions and wind wave prediction.

  13. Lipschitz Metrics for a Class of Nonlinear Wave Equations

    Science.gov (United States)

    Bressan, Alberto; Chen, Geng

    2017-12-01

    The nonlinear wave equation {u_{tt}-c(u)(c(u)u_x)_x=0} determines a flow of conservative solutions taking values in the space {H^1(R)}. However, this flow is not continuous with respect to the natural H 1 distance. The aim of this paper is to construct a new metric which renders the flow uniformly Lipschitz continuous on bounded subsets of {H^1(R)}. For this purpose, H 1 is given the structure of a Finsler manifold, where the norm of tangent vectors is defined in terms of an optimal transportation problem. For paths of piecewise smooth solutions, one can carefully estimate how the weighted length grows in time. By the generic regularity result proved in [7], these piecewise regular paths are dense and can be used to construct a geodesic distance with the desired Lipschitz property.

  14. A Priori Regularity of Parabolic Partial Differential Equations

    KAUST Repository

    Berkemeier, Francisco

    2018-05-13

    In this thesis, we consider parabolic partial differential equations such as the heat equation, the Fokker-Planck equation, and the porous media equation. Our aim is to develop methods that provide a priori estimates for solutions with singular initial data. These estimates are obtained by understanding the time decay of norms of solutions. First, we derive regularity results for the heat equation by estimating the decay of Lebesgue norms. Then, we apply similar methods to the Fokker-Planck equation with suitable assumptions on the advection and diffusion. Finally, we conclude by extending our techniques to the porous media equation. The sharpness of our results is confirmed by examining known solutions of these equations. The main contribution of this thesis is the use of functional inequalities to express decay of norms as differential inequalities. These are then combined with ODE methods to deduce estimates for the norms of solutions and their derivatives.

  15. Cnoidal waves governed by the Kudryashov–Sinelshchikov equation

    International Nuclear Information System (INIS)

    Randrüüt, Merle; Braun, Manfred

    2013-01-01

    The evolution equation for waves propagating in a mixture of liquid and gas bubbles as proposed by Kudryashov and Sinelshchikov allows, in a special case, the propagation of solitary waves of the sech 2 type. It is shown that these waves represent the solitary limit separating two families of periodic waves. One of them consists of the same cnoidal waves that are solutions of the Korteweg–de Vries equation, while the other one does not have a corresponding counterpart. It is pointed out how the ordinary differential equations governing traveling-wave solutions of the Kudryashov–Sinelshchikov and the Korteweg–de Vries equations are related to each other.

  16. Cnoidal waves governed by the Kudryashov–Sinelshchikov equation

    Energy Technology Data Exchange (ETDEWEB)

    Randrüüt, Merle, E-mail: merler@cens.ioc.ee [Tallinn University of Technology, Faculty of Mechanical Engineering, Department of Mechatronics, Ehitajate tee 5, 19086 Tallinn (Estonia); Braun, Manfred [University of Duisburg–Essen, Chair of Mechanics and Robotics, Lotharstraße 1, 47057 Duisburg (Germany)

    2013-10-30

    The evolution equation for waves propagating in a mixture of liquid and gas bubbles as proposed by Kudryashov and Sinelshchikov allows, in a special case, the propagation of solitary waves of the sech{sup 2} type. It is shown that these waves represent the solitary limit separating two families of periodic waves. One of them consists of the same cnoidal waves that are solutions of the Korteweg–de Vries equation, while the other one does not have a corresponding counterpart. It is pointed out how the ordinary differential equations governing traveling-wave solutions of the Kudryashov–Sinelshchikov and the Korteweg–de Vries equations are related to each other.

  17. A new auxiliary equation and exact travelling wave solutions of nonlinear equations

    International Nuclear Information System (INIS)

    Sirendaoreji

    2006-01-01

    A new auxiliary ordinary differential equation and its solutions are used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the auxiliary equation which has more new exact solutions. More new exact travelling wave solutions are obtained for the quadratic nonlinear Klein-Gordon equation, the combined KdV and mKdV equation, the sine-Gordon equation and the Whitham-Broer-Kaup equations

  18. Nonlinear Waves In A Stenosed Elastic Tube Filled With Viscous Fluid: Forced Perturbed Korteweg-De Vries Equation

    Science.gov (United States)

    Gaik*, Tay Kim; Demiray, Hilmi; Tiong, Ong Chee

    In the present work, treating the artery as a prestressed thin-walled and long circularly cylindrical elastic tube with a mild symmetrical stenosis and the blood as an incompressible Newtonian fluid, we have studied the pro pagation of weakly nonlinear waves in such a composite medium, in the long wave approximation, by use of the reductive perturbation method. By intro ducing a set of stretched coordinates suitable for the boundary value type of problems and expanding the field variables into asymptotic series of the small-ness parameter of nonlinearity and dispersion, we obtained a set of nonlinear differential equations governing the terms at various order. By solving these nonlinear differential equations, we obtained the forced perturbed Korteweg-de Vries equation with variable coefficient as the nonlinear evolution equation. By use of the coordinate transformation, it is shown that this type of nonlinear evolution equation admits a progressive wave solution with variable wave speed.

  19. Separate P‐ and SV‐wave equations for VTI media

    KAUST Repository

    Pestana, Reynam C.; Ursin, Bjø rn; Stoffa, Paul L.

    2011-01-01

    In isotropic media we use the scalar acoustic wave equation to perform reverse time migration RTM of the recorded pressure wavefleld data. In anisotropic media P- and SV-waves are coupled and the elastic wave equation should be used for RTM. However, an acoustic anisotropic wave equation is often used instead. This results in significant shear wave energy in both modeling and RTM. To avoid this undesired SV-wave energy, we propose a different approach to separate P- and SV-wave components for vertical transversely isotropic VTI media. We derive independent pseudo-differential wave equations for each mode. The derived equations for P- and SV-waves are stable and reduce to the isotropic case. The equations presented here can be effectively used to model and migrate seismic data in VTI media where ε - δ is small. The SV-wave equation we develop is now well-posed and triplications in the SV wavefront are removed resulting in stable wave propagation. We show modeling and RTM results using the derived pure P-wave mode in complex VTI media and use the rapid expansion method REM to propagate the waveflelds in time. © 2011 Society of Exploration Geophysicists.

  20. Wave Equation for Operators with Discrete Spectrum and Irregular Propagation Speed

    Science.gov (United States)

    Ruzhansky, Michael; Tokmagambetov, Niyaz

    2017-12-01

    Given a Hilbert space H, we investigate the well-posedness of the Cauchy problem for the wave equation for operators with a discrete non-negative spectrum acting on H. We consider the cases when the time-dependent propagation speed is regular, Hölder, and distributional. We also consider cases when it is strictly positive (strictly hyperbolic case) and when it is non-negative (weakly hyperbolic case). When the propagation speed is a distribution, we introduce the notion of "very weak solutions" to the Cauchy problem. We show that the Cauchy problem for the wave equation with the distributional coefficient has a unique "very weak solution" in an appropriate sense, which coincides with classical or distributional solutions when the latter exist. Examples include the harmonic and anharmonic oscillators, the Landau Hamiltonian on {R^n}, uniformly elliptic operators of different orders on domains, Hörmander's sums of squares on compact Lie groups and compact manifolds, operators on manifolds with boundary, and many others.

  1. Elastic Wave-equation Reflection Traveltime Inversion Using Dynamic Warping and Wave Mode Decomposition

    KAUST Repository

    Wang, T.

    2017-05-26

    Elastic full waveform inversion (EFWI) provides high-resolution parameter estimation of the subsurface but requires good initial guess of the true model. The traveltime inversion only minimizes traveltime misfits which are more sensitive and linearly related to the low-wavenumber model perturbation. Therefore, building initial P and S wave velocity models for EFWI by using elastic wave-equation reflections traveltime inversion (WERTI) would be effective and robust, especially for the deeper part. In order to distinguish the reflection travletimes of P or S-waves in elastic media, we decompose the surface multicomponent data into vector P- and S-wave seismogram. We utilize the dynamic image warping to extract the reflected P- or S-wave traveltimes. The P-wave velocity are first inverted using P-wave traveltime followed by the S-wave velocity inversion with S-wave traveltime, during which the wave mode decomposition is applied to the gradients calculation. Synthetic example on the Sigbee2A model proves the validity of our method for recovering the long wavelength components of the model.

  2. Solitary Wave Solutions of the Boussinesq Equation and Its Improved Form

    Directory of Open Access Journals (Sweden)

    Reza Abazari

    2013-01-01

    Full Text Available This paper presents the general case study of previous works on generalized Boussinesq equations, (Abazari, 2011 and (Kılıcman and Abazari, 2012, that focuses on the application of G′/G-expansion method with the aid of Maple to construct more general exact solutions for the coupled Boussinesq equations. In this work, the mentioned method is applied to construct more general exact solutions of Boussinesq equation and improved Boussinesq equation, which the French scientist Joseph Valentin Boussinesq (1842–1929 described in the 1870s model equations for the propagation of long waves on the surface of water with small amplitude. Our work is motivated by the fact that the G′/G-expansion method provides not only more general forms of solutions but also periodic, solitary waves and rational solutions. The method appears to be easier and faster by means of a symbolic computation.

  3. Regularized plane-wave least-squares Kirchhoff migration

    KAUST Repository

    Wang, Xin; Dai, Wei; Schuster, Gerard T.

    2013-01-01

    A Kirchhoff least-squares migration (LSM) is developed in the prestack plane-wave domain to increase the quality of migration images. A regularization term is included that accounts for mispositioning of reflectors due to errors in the velocity

  4. Study of nonlinear waves described by the cubic Schroedinger equation

    International Nuclear Information System (INIS)

    Walstead, A.E.

    1980-01-01

    The cubic Schroedinger equation (CSE) is ubiquitous as a model equation for the long-time evolution of finite-amplitude near-monochromatic dispersive waves. It incorporates the effects of the radiation field pressure on the constitutive properties of the supporting medium in a self-consistent manner. The properties of the uniformly transiating periodic wave solutions of the one-dimensional CSE are studied here. These (so-called cnoidal) waves are characterized by the values of four parameters. Whitham's averaged variational principle is used to derive a system of quasilinear evolution equations (the modulational equations) for the values of these parameters when they are slowly varying in space and time. Explicit expressions for the characteristic velocities of the modulational equations are obtained for the full set of cnoidal waves. Riemann invariants are obtained for several limits for the stable case, and growth rates are obtained for several limits, including the solitary wave chain, for the unstable case. The results for several nontrivial limiting cases agree with those obtained by independent methods by others. The dynamics of the CSE generalized to two spatial dimensions are studied for the unstable case. A large class of similarity solutions with cylindrical symmetry are obtained systematically using infinitesimal transformation group techniques. The methods are adapted to obtain the symmetries of the action functional of the CSE and to deduce nine integral invariants. A numerical study of the self-similar solutions reveals that they are modulationally unstable and that singularities dominate the dynamics of the CSE in two dimensions. The CSE is derived using perturbation theory for a specific problem in plasma physics: the evolution of the envelope of a near-monochromatic electromagnetic wave in a cold magnetized plasma. 13 figures, 2 tables

  5. Study of nonlinear waves described by the cubic Schroedinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Walstead, A.E.

    1980-03-12

    The cubic Schroedinger equation (CSE) is ubiquitous as a model equation for the long-time evolution of finite-amplitude near-monochromatic dispersive waves. It incorporates the effects of the radiation field pressure on the constitutive properties of the supporting medium in a self-consistent manner. The properties of the uniformly transiating periodic wave solutions of the one-dimensional CSE are studied here. These (so-called cnoidal) waves are characterized by the values of four parameters. Whitham's averaged variational principle is used to derive a system of quasilinear evolution equations (the modulational equations) for the values of these parameters when they are slowly varying in space and time. Explicit expressions for the characteristic velocities of the modulational equations are obtained for the full set of cnoidal waves. Riemann invariants are obtained for several limits for the stable case, and growth rates are obtained for several limits, including the solitary wave chain, for the unstable case. The results for several nontrivial limiting cases agree with those obtained by independent methods by others. The dynamics of the CSE generalized to two spatial dimensions are studied for the unstable case. A large class of similarity solutions with cylindrical symmetry are obtained systematically using infinitesimal transformation group techniques. The methods are adapted to obtain the symmetries of the action functional of the CSE and to deduce nine integral invariants. A numerical study of the self-similar solutions reveals that they are modulationally unstable and that singularities dominate the dynamics of the CSE in two dimensions. The CSE is derived using perturbation theory for a specific problem in plasma physics: the evolution of the envelope of a near-monochromatic electromagnetic wave in a cold magnetized plasma. 13 figures, 2 tables.

  6. Application of Littlewood-Paley decomposition to the regularity of Boltzmann type kinetic equations

    International Nuclear Information System (INIS)

    EL Safadi, M.

    2007-03-01

    We study the regularity of kinetic equations of Boltzmann type.We use essentially Littlewood-Paley method from harmonic analysis, consisting mainly in working with dyadics annulus. We shall mainly concern with the homogeneous case, where the solution f(t,x,v) depends only on the time t and on the velocities v, while working with realistic and singular cross-sections (non cutoff). In the first part, we study the particular case of Maxwellian molecules. Under this hypothesis, the structure of the Boltzmann operator and his Fourier transform write in a simple form. We show a global C ∞ regularity. Then, we deal with the case of general cross-sections with 'hard potential'. We are interested in the Landau equation which is limit equation to the Boltzmann equation, taking in account grazing collisions. We prove that any weak solution belongs to Schwartz space S. We demonstrate also a similar regularity for the case of Boltzmann equation. Let us note that our method applies directly for all dimensions, and proofs are often simpler compared to other previous ones. Finally, we finish with Boltzmann-Dirac equation. In particular, we adapt the result of regularity obtained in Alexandre, Desvillettes, Wennberg and Villani work, using the dissipation rate connected with Boltzmann-Dirac equation. (author)

  7. Blowing-up Semilinear Wave Equation with Exponential ...

    Indian Academy of Sciences (India)

    Blowing-up Semilinear Wave Equation with Exponential Nonlinearity in Two Space ... We investigate the initial value problem for some semi-linear wave equation in two space dimensions with exponential nonlinearity growth. ... Current Issue

  8. Orbital stability of solitary waves for Kundu equation

    Science.gov (United States)

    Zhang, Weiguo; Qin, Yinghao; Zhao, Yan; Guo, Boling

    In this paper, we consider the Kundu equation which is not a standard Hamiltonian system. The abstract orbital stability theory proposed by Grillakis et al. (1987, 1990) cannot be applied directly to study orbital stability of solitary waves for this equation. Motivated by the idea of Guo and Wu (1995), we construct three invariants of motion and use detailed spectral analysis to obtain orbital stability of solitary waves for Kundu equation. Since Kundu equation is more complex than the derivative Schrödinger equation, we utilize some techniques to overcome some difficulties in this paper. It should be pointed out that the results obtained in this paper are more general than those obtained by Guo and Wu (1995). We present a sufficient condition under which solitary waves are orbitally stable for 2c+sυ1995) only considered the case 2c+sυ>0. We obtain the results on orbital stability of solitary waves for the derivative Schrödinger equation given by Colin and Ohta (2006) as a corollary in this paper. Furthermore, we obtain orbital stability of solitary waves for Chen-Lee-Lin equation and Gerdjikov-Ivanov equation, respectively.

  9. An approach to rogue waves through the cnoidal equation

    Science.gov (United States)

    Lechuga, Antonio

    2014-05-01

    Lately it has been realized the importance of rogue waves in some events happening in open seas. Extreme waves and extreme weather could explain some accidents, but not all of them. Every now and then inflicted damages on ships only can be reported to be caused by anomalous and elusive waves, such as rogue waves. That's one of the reason why they continue attracting considerable interest among researchers. In the frame of the Nonlinear Schrödinger equation(NLS), Witham(1974) and Dingemans and Otta (2001)gave asymptotic solutions in moving coordinates that transformed the NLS equation in a ordinary differential equation that is the Duffing or cnoidal wave equation. Applying the Zakharov equation, Stiassnie and Shemer(2004) and Shemer(2010)got also a similar equation. It's well known that this ordinary equation can be solved in elliptic functions. The main aim of this presentation is to sort out the domains of the solutions of this equation, that, of course, are linked to the corresponding solutions of the partial differential equations(PDEs). That being, Lechuga(2007),a simple way to look for anomalous waves as it's the case with some "chaotic" solutions of the Duffing equation.

  10. Travelling wave solutions for a surface wave equation in fluid mechanics

    Directory of Open Access Journals (Sweden)

    Tian Yi

    2016-01-01

    Full Text Available This paper considers a non-linear wave equation arising in fluid mechanics. The exact traveling wave solutions of this equation are given by using G'/G-expansion method. This process can be reduced to solve a system of determining equations, which is large and difficult. To reduce this process, we used Wu elimination method. Example shows that this method is effective.

  11. Regularity criteria for the 3D magneto-micropolar fluid equations via ...

    Indian Academy of Sciences (India)

    3D magneto-micropolar fluid equations. It involves only the direction of the velocity and the magnetic field. Our result extends to the cases of Navier–Stokes and MHD equations. Keywords. Magneto-micropolar fluid equations; regularity criteria; direction of velocity. 2010 Mathematics Subject Classification. 35Q35, 76W05 ...

  12. Wave equations in higher dimensions

    CERN Document Server

    Dong, Shi-Hai

    2011-01-01

    Higher dimensional theories have attracted much attention because they make it possible to reduce much of physics in a concise, elegant fashion that unifies the two great theories of the 20th century: Quantum Theory and Relativity. This book provides an elementary description of quantum wave equations in higher dimensions at an advanced level so as to put all current mathematical and physical concepts and techniques at the reader’s disposal. A comprehensive description of quantum wave equations in higher dimensions and their broad range of applications in quantum mechanics is provided, which complements the traditional coverage found in the existing quantum mechanics textbooks and gives scientists a fresh outlook on quantum systems in all branches of physics. In Parts I and II the basic properties of the SO(n) group are reviewed and basic theories and techniques related to wave equations in higher dimensions are introduced. Parts III and IV cover important quantum systems in the framework of non-relativisti...

  13. Exact traveling wave solutions of the Boussinesq equation

    International Nuclear Information System (INIS)

    Ding Shuangshuang; Zhao Xiqiang

    2006-01-01

    The repeated homogeneous balance method is used to construct exact traveling wave solutions of the Boussinesq equation, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation, respectively. Many new exact traveling wave solutions of the Boussinesq equation are successfully obtained

  14. Viscous Regularization of the Euler Equations and Entropy Principles

    KAUST Repository

    Guermond, Jean-Luc

    2014-03-11

    This paper investigates a general class of viscous regularizations of the compressible Euler equations. A unique regularization is identified that is compatible with all the generalized entropies, à la [Harten et al., SIAM J. Numer. Anal., 35 (1998), pp. 2117-2127], and satisfies the minimum entropy principle. A connection with a recently proposed phenomenological model by [H. Brenner, Phys. A, 370 (2006), pp. 190-224] is made. © 2014 Society for Industrial and Applied Mathematics.

  15. Modelling and nonlinear shock waves for binary gas mixtures by the discrete Boltzmann equation with multiple collisions

    International Nuclear Information System (INIS)

    Bianchi, M.P.

    1991-01-01

    The discrete Boltzmann equation is a mathematical model in the kinetic theory of gases which defines the time and space evolution of a system of gas particles with a finite number of selected velocities. Discrete kinetic theory is an interesting field of research in mathematical physics and applied mathematics for several reasons. One of the relevant fields of application of the discrete Boltzmann equation is the analysis of nonlinear shock wave phenomena. Here, a new multiple collision regular plane model for binary gas mixtures is proposed within the discrete theory of gases and applied to the analysis of the classical problems of shock wave propagation

  16. On the wave equations with memory in noncylindrical domains

    Directory of Open Access Journals (Sweden)

    Mauro de Lima Santos

    2007-10-01

    Full Text Available In this paper we prove the exponential and polynomial decays rates in the case $n > 2$, as time approaches infinity of regular solutions of the wave equations with memory $$ u_{tt}-Delta u+int^{t}_{0}g(t-sDelta u(sds=0 quad mbox{in } widehat{Q} $$ where $widehat{Q}$ is a non cylindrical domains of $mathbb{R}^{n+1}$, $(nge1$. We show that the dissipation produced by memory effect is strong enough to produce exponential decay of solution provided the relaxation function $g$ also decays exponentially. When the relaxation function decay polynomially, we show that the solution decays polynomially with the same rate. For this we introduced a new multiplier that makes an important role in the obtaining of the exponential and polynomial decays of the energy of the system. Existence, uniqueness and regularity of solutions for any $n ge 1$ are investigated. The obtained result extends known results from cylindrical to non-cylindrical domains.

  17. Travelling wave solutions to the Kuramoto-Sivashinsky equation

    International Nuclear Information System (INIS)

    Nickel, J.

    2007-01-01

    Combining the approaches given by Baldwin [Baldwin D et al. Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs. J Symbol Comput 2004;37:669-705], Peng [Peng YZ. A polynomial expansion method and new general solitary wave solutions to KS equation. Comm Theor Phys 2003;39:641-2] and by Schuermann [Schuermann HW, Serov VS. Weierstrass' solutions to certain nonlinear wave and evolution equations. Proc progress electromagnetics research symposium, 28-31 March 2004, Pisa. p. 651-4; Schuermann HW. Traveling-wave solutions to the cubic-quintic nonlinear Schroedinger equation. Phys Rev E 1996;54:4312-20] leads to a method for finding exact travelling wave solutions of nonlinear wave and evolution equations (NLWEE). The first idea is to generalize ansaetze given by Baldwin and Peng to find elliptic solutions of NLWEEs. Secondly, conditions used by Schuermann to find physical (real and bounded) solutions and to discriminate between periodic and solitary wave solutions are used. The method is shown in detail by evaluating new solutions of the Kuramoto-Sivashinsky equation

  18. Wave-equation Q tomography

    KAUST Repository

    Dutta, Gaurav

    2016-10-12

    Strong subsurface attenuation leads to distortion of amplitudes and phases of seismic waves propagating inside the earth. The amplitude and the dispersion losses from attenuation are often compensated for during prestack depth migration. However, most attenuation compensation or Qcompensation migration algorithms require an estimate of the background Q model. We have developed a wave-equation gradient optimization method that inverts for the subsurface Q distribution by minimizing a skeletonized misfit function ∈, where ∈ is the sum of the squared differences between the observed and the predicted peak/centroid-frequency shifts of the early arrivals. The gradient is computed by migrating the observed traces weighted by the frequency shift residuals. The background Q model is perturbed until the predicted and the observed traces have the same peak frequencies or the same centroid frequencies. Numerical tests determined that an improved accuracy of the Q model by wave-equation Q tomography leads to a noticeable improvement in migration image quality. © 2016 Society of Exploration Geophysicists.

  19. Wave-equation Q tomography

    KAUST Repository

    Dutta, Gaurav; Schuster, Gerard T.

    2016-01-01

    Strong subsurface attenuation leads to distortion of amplitudes and phases of seismic waves propagating inside the earth. The amplitude and the dispersion losses from attenuation are often compensated for during prestack depth migration. However, most attenuation compensation or Qcompensation migration algorithms require an estimate of the background Q model. We have developed a wave-equation gradient optimization method that inverts for the subsurface Q distribution by minimizing a skeletonized misfit function ∈, where ∈ is the sum of the squared differences between the observed and the predicted peak/centroid-frequency shifts of the early arrivals. The gradient is computed by migrating the observed traces weighted by the frequency shift residuals. The background Q model is perturbed until the predicted and the observed traces have the same peak frequencies or the same centroid frequencies. Numerical tests determined that an improved accuracy of the Q model by wave-equation Q tomography leads to a noticeable improvement in migration image quality. © 2016 Society of Exploration Geophysicists.

  20. Traveling wave behavior for a generalized fisher equation

    International Nuclear Information System (INIS)

    Feng Zhaosheng

    2008-01-01

    There is the widespread existence of wave phenomena in physics, chemistry and biology. This clearly necessitates a study of traveling waves in depth and of the modeling and analysis involved. In the present paper, we study a nonlinear reaction-diffusion equation, which can be regarded as a generalized Fisher equation. Applying the Cole-Hopf transformation and the first integral method, we obtain a class of traveling solitary wave solutions for this generalized Fisher equation

  1. Parsimonious wave-equation travel-time inversion for refraction waves

    KAUST Repository

    Fu, Lei; Hanafy, Sherif M.; Schuster, Gerard T.

    2017-01-01

    We present a parsimonious wave-equation travel-time inversion technique for refraction waves. A dense virtual refraction dataset can be generated from just two reciprocal shot gathers for the sources at the endpoints of the survey line, with N

  2. Exact traveling wave solutions of modified KdV-Zakharov-Kuznetsov equation and viscous Burgers equation.

    Science.gov (United States)

    Islam, Md Hamidul; Khan, Kamruzzaman; Akbar, M Ali; Salam, Md Abdus

    2014-01-01

    Mathematical modeling of many physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear partial differential equations (NPDEs) plays a significant role in the study of nonlinear physical phenomena. In this article, we construct the traveling wave solutions of modified KDV-ZK equation and viscous Burgers equation by using an enhanced (G '/G) -expansion method. A number of traveling wave solutions in terms of unknown parameters are obtained. Derived traveling wave solutions exhibit solitary waves when special values are given to its unknown parameters. 35C07; 35C08; 35P99.

  3. Solitary-wave families of the Ostrovsky equation: An approach via reversible systems theory and normal forms

    International Nuclear Information System (INIS)

    Roy Choudhury, S.

    2007-01-01

    The Ostrovsky equation is an important canonical model for the unidirectional propagation of weakly nonlinear long surface and internal waves in a rotating, inviscid and incompressible fluid. Limited functional analytic results exist for the occurrence of one family of solitary-wave solutions of this equation, as well as their approach to the well-known solitons of the famous Korteweg-de Vries equation in the limit as the rotation becomes vanishingly small. Since solitary-wave solutions often play a central role in the long-time evolution of an initial disturbance, we consider such solutions here (via the normal form approach) within the framework of reversible systems theory. Besides confirming the existence of the known family of solitary waves and its reduction to the KdV limit, we find a second family of multihumped (or N-pulse) solutions, as well as a continuum of delocalized solitary waves (or homoclinics to small-amplitude periodic orbits). On isolated curves in the relevant parameter region, the delocalized waves reduce to genuine embedded solitons. The second and third families of solutions occur in regions of parameter space distinct from the known solitary-wave solutions and are thus entirely new. Directions for future work are also mentioned

  4. Wave-equation reflection traveltime inversion

    KAUST Repository

    Zhang, Sanzong

    2011-01-01

    The main difficulty with iterative waveform inversion using a gradient optimization method is that it tends to get stuck in local minima associated within the waveform misfit function. This is because the waveform misfit function is highly nonlinear with respect to changes in the velocity model. To reduce this nonlinearity, we present a reflection traveltime tomography method based on the wave equation which enjoys a more quasi-linear relationship between the model and the data. A local crosscorrelation of the windowed downgoing direct wave and the upgoing reflection wave at the image point yields the lag time that maximizes the correlation. This lag time represents the reflection traveltime residual that is back-projected into the earth model to update the velocity in the same way as wave-equation transmission traveltime inversion. No travel-time picking is needed and no high-frequency approximation is assumed. The mathematical derivation and the numerical examples are presented to partly demonstrate its efficiency and robustness. © 2011 Society of Exploration Geophysicists.

  5. Unsplit complex frequency shifted perfectly matched layer for second-order wave equation using auxiliary differential equations.

    Science.gov (United States)

    Gao, Yingjie; Zhang, Jinhai; Yao, Zhenxing

    2015-12-01

    The complex frequency shifted perfectly matched layer (CFS-PML) can improve the absorbing performance of PML for nearly grazing incident waves. However, traditional PML and CFS-PML are based on first-order wave equations; thus, they are not suitable for second-order wave equation. In this paper, an implementation of CFS-PML for second-order wave equation is presented using auxiliary differential equations. This method is free of both convolution calculations and third-order temporal derivatives. As an unsplit CFS-PML, it can reduce the nearly grazing incidence. Numerical experiments show that it has better absorption than typical PML implementations based on second-order wave equation.

  6. Integral equations of the first kind, inverse problems and regularization: a crash course

    International Nuclear Information System (INIS)

    Groetsch, C W

    2007-01-01

    This paper is an expository survey of the basic theory of regularization for Fredholm integral equations of the first kind and related background material on inverse problems. We begin with an historical introduction to the field of integral equations of the first kind, with special emphasis on model inverse problems that lead to such equations. The basic theory of linear Fredholm equations of the first kind, paying particular attention to E. Schmidt's singular function analysis, Picard's existence criterion, and the Moore-Penrose theory of generalized inverses is outlined. The fundamentals of the theory of Tikhonov regularization are then treated and a collection of exercises and a bibliography are provided

  7. Regular and chaotic behaviors of plasma oscillations modeled by a modified Duffing equation

    International Nuclear Information System (INIS)

    Enjieu Kadji, H.G.; Chabi Orou, J.B.; Woafo, P.; Abdus Salam International Centre for Theoretical Physics, Trieste

    2005-07-01

    The regular and chaotic behavior of plasma oscillations governed by a modified Duffing equation is studied. The plasma oscillations are described by a nonlinear differential equation of the form x + w 0 2 x + βx 2 + αx 3 = 0 which is similar to a Duffing equation. By focusing on the quadratic term, which is mainly the term modifying the Duffing equation, the harmonic balance method and the fourth order Runge-Kutta algorithm are used to derive regular and chaotic motions respectively. A strong chaotic behavior exhibited by the system in that event when the system is subjected to an external periodic forcing oscillation is reported as β varies. (author)

  8. Paraxial WKB solution of a scalar wave equation

    International Nuclear Information System (INIS)

    Pereverzev, G.V.

    1993-04-01

    An asymptotic method of solving a scalar wave equation in inhomogeneous media is developed. This method is an extension of the WKB method to the multidimensional case. It reduces a general wave equation to a set of ordinary differential equations similar to that of the eikonal approach and includes the latter as a particular case. However, the WKB method makes use of another kind of asymptotic expansion and, unlike the eikonal approach, describes the wave properties, i.e. diffraction and interference. At the same time, the three-dimensional WKB method is more simple for numerical treatment because the number of equations is less than in the eikonal approach. The method developed may be used for a calculation of wave fields in problems of RF heating, current drive and plasma diagnostics with microwave beams. (orig.)

  9. N-body bound state relativistic wave equations

    International Nuclear Information System (INIS)

    Sazdjian, H.

    1988-06-01

    The manifestly covariant formalism with constraints is used for the construction of relativistic wave equations to describe the dynamics of N interacting spin 0 and/or spin 1/2 particles. The total and relative time evolutions of the system are completely determined by means of kinematic type wave equations. The internal dynamics of the system is 3 N-1 dimensional, besides the contribution of the spin degrees of freedom. It is governed by a single dynamical wave equation, that determines the eigenvalue of the total mass squared of the system. The interaction is introduced in a closed form by means of two-body potentials. The system satisfies an approximate form of separability

  10. Modified wave operators for nonlinear Schrodinger equations in one and two dimensions

    Directory of Open Access Journals (Sweden)

    Nakao Hayashi

    2004-04-01

    Full Text Available We study the asymptotic behavior of solutions, in particular the scattering theory, for the nonlinear Schr"{o}dinger equations with cubic and quadratic nonlinearities in one or two space dimensions. The nonlinearities are summation of gauge invariant term and non-gauge invariant terms. The scattering problem of these equations belongs to the long range case. We prove the existence of the modified wave operators to those equations for small final data. Our result is an improvement of the previous work [13

  11. Regularity of the 3D Navier-Stokes equations with viewpoint of 2D flow

    Science.gov (United States)

    Bae, Hyeong-Ohk

    2018-04-01

    The regularity of 2D Navier-Stokes flow is well known. In this article we study the relationship of 3D and 2D flow, and the regularity of the 3D Naiver-Stokes equations with viewpoint of 2D equations. We consider the problem in the Cartesian and in the cylindrical coordinates.

  12. Solution of the Helmholtz-Poincare Wave Equation using the coupled boundary integral equations and optimal surface eigenfunctions

    International Nuclear Information System (INIS)

    Werby, M.F.; Broadhead, M.K.; Strayer, M.R.; Bottcher, C.

    1992-01-01

    The Helmholtz-Poincarf Wave Equation (H-PWE) arises in many areas of classical wave scattering theory. In particular it can be found for the cases of acoustical scattering from submerged bounded objects and electromagnetic scattering from objects. The extended boundary integral equations (EBIE) method is derived from considering both the exterior and interior solutions of the H-PWECs. This coupled set of expressions has the advantage of not only offering a prescription for obtaining a solution for the exterior scattering problem, but it also obviates the problem of irregular values corresponding to fictitious interior eigenvalues. Once the coupled equations are derived, they can be obtained in matrix form by expanding all relevant terms in partial wave expansions, including a bi-orthogonal expansion of the Green's function. However some freedom in the choice of the surface expansion is available since the unknown surface quantities may be expanded in a variety of ways so long as closure is obtained. Out of many possible choices, we develop an optimal method to obtain such expansions which is based on the optimum eigenfunctions related to the surface of the object. In effect, we convert part of the problem (that associated with the Fredholms integral equation of the first kind) an eigenvalue problem of a related Hermitian operator. The methodology will be explained in detail and examples will be presented

  13. Wave-equation dispersion inversion

    KAUST Repository

    Li, Jing; Feng, Zongcai; Schuster, Gerard T.

    2016-01-01

    We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained

  14. Temperature waves and the Boltzmann kinetic equation for phonons

    International Nuclear Information System (INIS)

    Urushev, D.; Borisov, M.; Vavrek, A.

    1988-01-01

    The ordinary parabolic equation for thermal conduction based on the Fourier empiric law as well as the generalized thermal conduction equation based on the Maxwell law have been derived from the Boltzmann equation for the phonons within the relaxation time approximation. The temperature waves of the so-called second sound in crystals at low temperatures are transformed into Fourier waves at low frequencies with respect to the characteristic frequency of the U-processes. These waves are transformed into temperature waves similar to the second sound waves in He II at frequences higher than the U-processes characteristic. 1 fig., 19 refs

  15. Regularization algorithm within two-parameters for identification heat-coefficient in the parabolic equation

    International Nuclear Information System (INIS)

    Hinestroza Gutierrez, D.

    2006-08-01

    In this work a new and promising algorithm based on the minimization of especial functional that depends on two regularization parameters is considered for the identification of the heat conduction coefficient in the parabolic equation. This algorithm uses the adjoint and sensibility equations. One of the regularization parameters is associated with the heat-coefficient (as in conventional Tikhonov algorithms) but the other is associated with the calculated solution. (author)

  16. Regularization algorithm within two-parameters for identification heat-coefficient in the parabolic equation

    International Nuclear Information System (INIS)

    Hinestroza Gutierrez, D.

    2006-12-01

    In this work a new and promising algorithm based in the minimization of especial functional that depends on two regularization parameters is considered for identification of the heat conduction coefficient in the parabolic equation. This algorithm uses the adjoint and sensibility equations. One of the regularization parameters is associated with the heat-coefficient (as in conventional Tikhonov algorithms) but the other is associated with the calculated solution. (author)

  17. A new sub-equation method applied to obtain exact travelling wave solutions of some complex nonlinear equations

    International Nuclear Information System (INIS)

    Zhang Huiqun

    2009-01-01

    By using a new coupled Riccati equations, a direct algebraic method, which was applied to obtain exact travelling wave solutions of some complex nonlinear equations, is improved. And the exact travelling wave solutions of the complex KdV equation, Boussinesq equation and Klein-Gordon equation are investigated using the improved method. The method presented in this paper can also be applied to construct exact travelling wave solutions for other nonlinear complex equations.

  18. Exact solitary waves of the Fisher equation

    International Nuclear Information System (INIS)

    Kudryashov, Nikolai A.

    2005-01-01

    New method is presented to search exact solutions of nonlinear differential equations. This approach is used to look for exact solutions of the Fisher equation. New exact solitary waves of the Fisher equation are given

  19. Skeletonized Least Squares Wave Equation Migration

    KAUST Repository

    Zhan, Ge

    2010-10-17

    The theory for skeletonized least squares wave equation migration (LSM) is presented. The key idea is, for an assumed velocity model, the source‐side Green\\'s function and the geophone‐side Green\\'s function are computed by a numerical solution of the wave equation. Only the early‐arrivals of these Green\\'s functions are saved and skeletonized to form the migration Green\\'s function (MGF) by convolution. Then the migration image is obtained by a dot product between the recorded shot gathers and the MGF for every trial image point. The key to an efficient implementation of iterative LSM is that at each conjugate gradient iteration, the MGF is reused and no new finitedifference (FD) simulations are needed to get the updated migration image. It is believed that this procedure combined with phase‐encoded multi‐source technology will allow for the efficient computation of wave equation LSM images in less time than that of conventional reverse time migration (RTM).

  20. Super-Grid Modeling of the Elastic Wave Equation in Semi-Bounded Domains

    Energy Technology Data Exchange (ETDEWEB)

    Petersson, N. Anders; Sjögreen, Björn

    2014-10-01

    Abstract

    We develop a super-grid modeling technique for solving the elastic wave equation in semi-bounded two- and three-dimensional spatial domains. In this method, waves are slowed down and dissipated in sponge layers near the far-field boundaries. Mathematically, this is equivalent to a coordinate mapping that transforms a very large physical domain to a significantly smaller computational domain, where the elastic wave equation is solved numerically on a regular grid. To damp out waves that become poorly resolved because of the coordinate mapping, a high order artificial dissipation operator is added in layers near the boundaries of the computational domain. We prove by energy estimates that the super-grid modeling leads to a stable numerical method with decreasing energy, which is valid for heterogeneous material properties and a free surface boundary condition on one side of the domain. Our spatial discretization is based on a fourth order accurate finite difference method, which satisfies the principle of summation by parts. We show that the discrete energy estimate holds also when a centered finite difference stencil is combined with homogeneous Dirichlet conditions at several ghost points outside of the far-field boundaries. Therefore, the coefficients in the finite difference stencils need only be boundary modified near the free surface. This allows for improved computational efficiency and significant simplifications of the implementation of the proposed method in multi-dimensional domains. Numerical experiments in three space dimensions show that the modeling error from truncating the domain can be made very small by choosing a sufficiently wide super-grid damping layer. The numerical accuracy is first evaluated against analytical solutions of Lamb’s problem, where fourth order accuracy is observed with a sixth order artificial dissipation. We then use successive grid refinements to study the numerical accuracy in the more

  1. Gabor Wave Packet Method to Solve Plasma Wave Equations

    International Nuclear Information System (INIS)

    Pletzer, A.; Phillips, C.K.; Smithe, D.N.

    2003-01-01

    A numerical method for solving plasma wave equations arising in the context of mode conversion between the fast magnetosonic and the slow (e.g ion Bernstein) wave is presented. The numerical algorithm relies on the expansion of the solution in Gaussian wave packets known as Gabor functions, which have good resolution properties in both real and Fourier space. The wave packets are ideally suited to capture both the large and small wavelength features that characterize mode conversion problems. The accuracy of the scheme is compared with a standard finite element approach

  2. Initial-Boundary Value Problem Solution of the Nonlinear Shallow-water Wave Equations

    Science.gov (United States)

    Kanoglu, U.; Aydin, B.

    2014-12-01

    The hodograph transformation solutions of the one-dimensional nonlinear shallow-water wave (NSW) equations are usually obtained through integral transform techniques such as Fourier-Bessel transforms. However, the original formulation of Carrier and Greenspan (1958 J Fluid Mech) and its variant Carrier et al. (2003 J Fluid Mech) involve evaluation integrals. Since elliptic integrals are highly singular as discussed in Carrier et al. (2003), this solution methodology requires either approximation of the associated integrands by smooth functions or selection of regular initial/boundary data. It should be noted that Kanoglu (2004 J Fluid Mech) partly resolves this issue by simplifying the resulting integrals in closed form. Here, the hodograph transform approach is coupled with the classical eigenfunction expansion method rather than integral transform techniques and a new analytical model for nonlinear long wave propagation over a plane beach is derived. This approach is based on the solution methodology used in Aydın & Kanoglu (2007 CMES-Comp Model Eng) for wind set-down relaxation problem. In contrast to classical initial- or boundary-value problem solutions, here, the NSW equations are formulated to yield an initial-boundary value problem (IBVP) solution. In general, initial wave profile with nonzero initial velocity distribution is assumed and the flow variables are given in the form of Fourier-Bessel series. The results reveal that the developed method allows accurate estimation of the spatial and temporal variation of the flow quantities, i.e., free-surface height and depth-averaged velocity, with much less computational effort compared to the integral transform techniques such as Carrier et al. (2003), Kanoglu (2004), Tinti & Tonini (2005 J Fluid Mech), and Kanoglu & Synolakis (2006 Phys Rev Lett). Acknowledgments: This work is funded by project ASTARTE- Assessment, STrategy And Risk Reduction for Tsunamis in Europe. Grant 603839, 7th FP (ENV.2013.6.4-3 ENV

  3. Diffusion phenomenon for linear dissipative wave equations

    KAUST Repository

    Said-Houari, Belkacem

    2012-01-01

    In this paper we prove the diffusion phenomenon for the linear wave equation. To derive the diffusion phenomenon, a new method is used. In fact, for initial data in some weighted spaces, we prove that for {equation presented} decays with the rate {equation presented} [0,1] faster than that of either u or v, where u is the solution of the linear wave equation with initial data {equation presented} [0,1], and v is the solution of the related heat equation with initial data v 0 = u 0 + u 1. This result improves the result in H. Yang and A. Milani [Bull. Sci. Math. 124 (2000), 415-433] in the sense that, under the above restriction on the initial data, the decay rate given in that paper can be improved by t -γ/2. © European Mathematical Society.

  4. On Long-Time Instabilities in Staggered Finite Difference Simulations of the Seismic Acoustic Wave Equations on Discontinuous Grids

    KAUST Repository

    Gao, Longfei

    2017-10-26

    We consider the long-time instability issue associated with finite difference simulation of seismic acoustic wave equations on discontinuous grids. This issue is exhibited by a prototype algebraic problem abstracted from practical application settings. Analysis of this algebraic problem leads to better understanding of the cause of the instability and provides guidance for its treatment. Specifically, we use the concept of discrete energy to derive the proper solution transfer operators and design an effective way to damp the unstable solution modes. Our investigation shows that the interpolation operators need to be matched with their companion restriction operators in order to properly couple the coarse and fine grids. Moreover, to provide effective damping, specially designed diffusive terms are introduced to the equations at designated locations and discretized with specially designed schemes. These techniques are applied to simulations in practical settings and are shown to lead to superior results in terms of both stability and accuracy.

  5. On long-time instabilities in staggered finite difference simulations of the seismic acoustic wave equations on discontinuous grids

    Science.gov (United States)

    Gao, Longfei; Ketcheson, David; Keyes, David

    2018-02-01

    We consider the long-time instability issue associated with finite difference simulation of seismic acoustic wave equations on discontinuous grids. This issue is exhibited by a prototype algebraic problem abstracted from practical application settings. Analysis of this algebraic problem leads to better understanding of the cause of the instability and provides guidance for its treatment. Specifically, we use the concept of discrete energy to derive the proper solution transfer operators and design an effective way to damp the unstable solution modes. Our investigation shows that the interpolation operators need to be matched with their companion restriction operators in order to properly couple the coarse and fine grids. Moreover, to provide effective damping, specially designed diffusive terms are introduced to the equations at designated locations and discretized with specially designed schemes. These techniques are applied to simulations in practical settings and are shown to lead to superior results in terms of both stability and accuracy.

  6. Nonlinear Electrostatic Wave Equations for Magnetized Plasmas

    DEFF Research Database (Denmark)

    Dysthe, K.B.; Mjølhus, E.; Pécseli, Hans

    1984-01-01

    The lowest order kinetic effects are included in the equations for nonlinear electrostatic electron waves in a magnetized plasma. The modifications of the authors' previous analysis based on a fluid model are discussed.......The lowest order kinetic effects are included in the equations for nonlinear electrostatic electron waves in a magnetized plasma. The modifications of the authors' previous analysis based on a fluid model are discussed....

  7. Bifurcations of traveling wave solutions for an integrable equation

    International Nuclear Information System (INIS)

    Li Jibin; Qiao Zhijun

    2010-01-01

    This paper deals with the following equation m t =(1/2)(1/m k ) xxx -(1/2)(1/m k ) x , which is proposed by Z. J. Qiao [J. Math. Phys. 48, 082701 (2007)] and Qiao and Liu [Chaos, Solitons Fractals 41, 587 (2009)]. By adopting the phase analysis method of planar dynamical systems and the theory of the singular traveling wave systems to the traveling wave solutions of the equation, it is shown that for different k, the equation may have infinitely many solitary wave solutions, periodic wave solutions, kink/antikink wave solutions, cusped solitary wave solutions, and breaking loop solutions. We discuss in a detail the cases of k=-2,-(1/2),(1/2),2, and parametric representations of all possible bounded traveling wave solutions are given in the different (c,g)-parameter regions.

  8. Family of electrovac colliding wave solutions of Einstein's equations

    International Nuclear Information System (INIS)

    Li, W.; Ernst, F.J.

    1989-01-01

    Beginning with any colliding wave solution of the vacuum Einstein equations, a corresponding electrified colliding wave solution can be generated through the use of a transformation due to Harrison [J. Math. Phys. 9, 1744 (1968)]. The method, long employed in the context of stationary axisymmetric fields, is equally applicable to colliding wave solutions. Here it is applied to a large family of vacuum metrics derived by applying a generalized Ehlers transformation to solutions published recently by Ernst, Garcia, and Hauser (EGH) [J. Math. Phys. 28, 2155, 2951 (1987); 29, 681 (1988)]. Those EGH solutions were themselves a generalization of solutions first derived by Ferrari, Ibanez, and Bruni [Phys. Rev. D 36, 1053 (1987)]. Among the electrovac solutions that are obtained is a charged version of the Nutku--Halil [Phys. Rev. Lett. 39, 1379 (1977)] metric that possesses an arbitrary complex charge parameter

  9. Stability of Planar Rarefaction Wave to 3D Full Compressible Navier-Stokes Equations

    Science.gov (United States)

    Li, Lin-an; Wang, Teng; Wang, Yi

    2018-05-01

    We prove time-asymptotic stability toward the planar rarefaction wave for the three-dimensional full, compressible Navier-Stokes equations with the heat-conductivities in an infinite long flat nozzle domain {R × T^2} . Compared with one-dimensional case, the proof here is based on our new observations on the cancellations on the flux terms and viscous terms due to the underlying wave structures, which are crucial for overcoming the difficulties due to the wave propagation in the transverse directions x 2 and x 3 and its interactions with the planar rarefaction wave in x 1 direction.

  10. Capillary-gravity waves and the Navier-Stokes equation

    International Nuclear Information System (INIS)

    Behroozi, F.; Podolefsky, N.

    2001-01-01

    Water waves are a source of great fascination for undergraduates and thus provide an excellent context for introducing some important topics in fluid dynamics. In this paper we introduce the potential theory for incompressible and inviscid flow and derive the differential equation that governs the behaviour of the velocity potential. Next we obtain the harmonic solutions of the velocity potential by a very general argument. These solutions in turn yield the equations for the velocity and displacement of a water element under the action of a harmonic wave. Finally we obtain the dispersion relation for surface waves by requiring that the harmonic solutions satisfy the Navier-Stokes equation. (author)

  11. A new iterative solver for the time-harmonic wave equation

    NARCIS (Netherlands)

    Riyanti, C.D.; Erlangga, Y.A.; Plessix, R.E.; Mulder, W.A.; Vuik, C.; Oosterlee, C.

    2006-01-01

    The time-harmonic wave equation, also known as the Helmholtz equation, is obtained if the constant-density acoustic wave equation is transformed from the time domain to the frequency domain. Its discretization results in a large, sparse, linear system of equations. In two dimensions, this system can

  12. On the regularity criterion of weak solutions for the 3D MHD equations

    Science.gov (United States)

    Gala, Sadek; Ragusa, Maria Alessandra

    2017-12-01

    The paper deals with the 3D incompressible MHD equations and aims at improving a regularity criterion in terms of the horizontal gradient of velocity and magnetic field. It is proved that the weak solution ( u, b) becomes regular provided that ( \

  13. An acoustic wave equation for pure P wave in 2D TTI media

    KAUST Repository

    Zhan, Ge; Pestana, Reynam C.; Stoffa, Paul L.

    2011-01-01

    In this paper, a pure P wave equation for an acoustic 2D TTI media is derived. Compared with conventional TTI coupled equations, the resulting equation is unconditionally stable due to the complete isolation of the SV wave mode. To avoid numerical dispersion and produce high quality images, the rapid expansion method REM is employed for numerical implementation. Synthetic results validate the proposed equation and show that it is a stable algorithm for modeling and reverse time migration RTM in a TTI media for any anisotropic parameter values. © 2011 Society of Exploration Geophysicists.

  14. A study of wave forces on an offshore platform by direct CFD and Morison equation

    Directory of Open Access Journals (Sweden)

    Zhang D.

    2015-01-01

    The next step is the presentation of 3D multiphase RANS simulation of the wind-turbine platform in single-harmonic regular waves. Simulation results from full 3D simulation will be compared to the results from Morison’s equation. We are motivated by the challenges of a floating platform which has complex underwater geometry (e.g. tethered semi-submersible. In cases like this, our hypothesis is that Morison’s equation will result in inaccurate prediction of forces, due to the limitations of 2D coefficients of simple geometries, and that 3D multiphase RANS CFD will be required to generate reliable predictions of platform loads and motions.

  15. Multiple travelling wave solutions of nonlinear evolution equations using a unified algebraic method

    International Nuclear Information System (INIS)

    Fan Engui

    2002-01-01

    A new direct and unified algebraic method for constructing multiple travelling wave solutions of general nonlinear evolution equations is presented and implemented in a computer algebraic system. Compared with most of the existing tanh methods, the Jacobi elliptic function method or other sophisticated methods, the proposed method not only gives new and more general solutions, but also provides a guideline to classify the various types of the travelling wave solutions according to the values of some parameters. The solutions obtained in this paper include (a) kink-shaped and bell-shaped soliton solutions, (b) rational solutions, (c) triangular periodic solutions and (d) Jacobi and Weierstrass doubly periodic wave solutions. Among them, the Jacobi elliptic periodic wave solutions exactly degenerate to the soliton solutions at a certain limit condition. The efficiency of the method can be demonstrated on a large variety of nonlinear evolution equations such as those considered in this paper, KdV-MKdV, Ito's fifth MKdV, Hirota, Nizhnik-Novikov-Veselov, Broer-Kaup, generalized coupled Hirota-Satsuma, coupled Schroedinger-KdV, (2+1)-dimensional dispersive long wave, (2+1)-dimensional Davey-Stewartson equations. In addition, as an illustrative sample, the properties of the soliton solutions and Jacobi doubly periodic solutions for the Hirota equation are shown by some figures. The links among our proposed method, the tanh method, extended tanh method and the Jacobi elliptic function method are clarified generally. (author)

  16. Analysis and Computation of Acoustic and Elastic Wave Equations in Random Media

    KAUST Repository

    Motamed, Mohammad

    2014-01-06

    We propose stochastic collocation methods for solving the second order acoustic and elastic wave equations in heterogeneous random media and subject to deterministic boundary and initial conditions [1, 4]. We assume that the medium consists of non-overlapping sub-domains with smooth interfaces. In each sub-domain, the materials coefficients are smooth and given or approximated by a finite number of random variable. One important example is wave propagation in multi-layered media with smooth interfaces. The numerical scheme consists of a finite difference or finite element method in the physical space and a collocation in the zeros of suitable tensor product orthogonal polynomials (Gauss points) in the probability space. We provide a rigorous convergence analysis and demonstrate different types of convergence of the probability error with respect to the number of collocation points under some regularity assumptions on the data. In particular, we show that, unlike in elliptic and parabolic problems [2, 3], the solution to hyperbolic problems is not in general analytic with respect to the random variables. Therefore, the rate of convergence is only algebraic. A fast spectral rate of convergence is still possible for some quantities of interest and for the wave solutions with particular types of data. We also show that the semi-discrete solution is analytic with respect to the random variables with the radius of analyticity proportional to the grid/mesh size h. We therefore obtain an exponential rate of convergence which deteriorates as the quantity h p gets smaller, with p representing the polynomial degree in the stochastic space. We have shown that analytical results and numerical examples are consistent and that the stochastic collocation method may be a valid alternative to the more traditional Monte Carlo method. Here we focus on the stochastic acoustic wave equation. Similar results are obtained for stochastic elastic equations.

  17. Relativistic wave equations and compton scattering

    International Nuclear Information System (INIS)

    Sutanto, S.H.; Robson, B.A.

    1998-01-01

    Full text: Recently an eight-component relativistic wave equation for spin-1/2 particles was proposed.This equation was obtained from a four-component spin-1/2 wave equation (the KG1/2 equation), which contains second-order derivatives in both space and time, by a procedure involving a linearisation of the time derivative analogous to that introduced by Feshbach and Villars for the Klein-Gordon equation. This new eight-component equation gives the same bound-state energy eigenvalue spectra for hydrogenic atoms as the Dirac equation but has been shown to predict different radiative transition probabilities for the fine structure of both the Balmer and Lyman a-lines. Since it has been shown that the new theory does not always give the same results as the Dirac theory, it is important to consider the validity of the new equation in the case of other physical problems. One of the early crucial tests of the Dirac theory was its application to the scattering of a photon by a free electron: the so-called Compton scattering problem. In this paper we apply the new theory to the calculation of Compton scattering to order e 2 . It will be shown that in spite of the considerable difference in the structure of the new theory and that of Dirac the cross section is given by the Klein-Nishina formula

  18. EXACT TRAVELLING WAVE SOLUTIONS TO BBM EQUATION

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    Abundant new travelling wave solutions to the BBM (Benjamin-Bona-Mahoni) equation are obtained by the generalized Jacobian elliptic function method. This method can be applied to other nonlinear evolution equations.

  19. Correct Linearization of Einstein's Equations

    Directory of Open Access Journals (Sweden)

    Rabounski D.

    2006-06-01

    Full Text Available Regularly Einstein's equations can be reduced to a wave form (linearly dependent from the second derivatives of the space metric in the absence of gravitation, the space rotation and Christoffel's symbols. As shown here, the origin of the problem is that one uses the general covariant theory of measurement. Here the wave form of Einstein's equations is obtained in the terms of Zelmanov's chronometric invariants (physically observable projections on the observer's time line and spatial section. The obtained equations depend on solely the second derivatives even if gravitation, the space rotation and Christoffel's symbols. The correct linearization proves: the Einstein equations are completely compatible with weak waves of the metric.

  20. A wave equation interpolating between classical and quantum mechanics

    Science.gov (United States)

    Schleich, W. P.; Greenberger, D. M.; Kobe, D. H.; Scully, M. O.

    2015-10-01

    We derive a ‘master’ wave equation for a family of complex-valued waves {{Φ }}\\equiv R{exp}[{{{i}}S}({cl)}/{{\\hbar }}] whose phase dynamics is dictated by the Hamilton-Jacobi equation for the classical action {S}({cl)}. For a special choice of the dynamics of the amplitude R which eliminates all remnants of classical mechanics associated with {S}({cl)} our wave equation reduces to the Schrödinger equation. In this case the amplitude satisfies a Schrödinger equation analogous to that of a charged particle in an electromagnetic field where the roles of the scalar and the vector potentials are played by the classical energy and the momentum, respectively. In general this amplitude is complex and thereby creates in addition to the classical phase {S}({cl)}/{{\\hbar }} a quantum phase. Classical statistical mechanics, as described by a classical matter wave, follows from our wave equation when we choose the dynamics of the amplitude such that it remains real for all times. Our analysis shows that classical and quantum matter waves are distinguished by two different choices of the dynamics of their amplitudes rather than two values of Planck’s constant. We dedicate this paper to the memory of Richard Lewis Arnowitt—a pioneer of many-body theory, a path finder at the interface of gravity and quantum mechanics, and a true leader in non-relativistic and relativistic quantum field theory.

  1. Long gravitational waves in a closed universe

    International Nuclear Information System (INIS)

    Grishchuk, L.P.; Doroshkevich, A.G.; Yudin, V.M.

    The important part played by long gravitational waves in the evolution of a homogeneous closed universe (model of type IX in Biancki's classification) is discussed. It is shown that the metric of this model can be represented in the form of a sum of a background metric, describing nonstationary space of constant positive curvature, and a group of terms that may be interpreted as a set of gravitational waves of maximal length compatible with closure of the space. This subdivision of the metric is exact and does not presuppose necessary smallness of the wave corrections. For this reason the behavior of the wave terms can be traced at all stages of their evolution--both in the epoch when the contribution of the ''energy density'' and ''pressure'' of the gravitational waves to the dynamics of the background universe is negligibly small and in the epoch when this contribution is dominant. It was demonstrated, in particular, that in the limiting case of complete absence of ordinary matter the scale factor of the background metric, because of the negativity of gravitational ''pressure,''can pass during the evolution of the universe through a state of stable regular minimum

  2. Forcing of a bottom-mounted circular cylinder by steep regular water waves at finite depth

    DEFF Research Database (Denmark)

    Paulsen, Bo Terp; Bredmose, Henrik; Bingham, Harry B.

    2014-01-01

    of secondary load cycles. Special attention was paid to this secondary load cycle and the flow features that cause it. By visual observation and a simplified analytical model it was shown that the secondary load cycle was caused by the strong nonlinear motion of the free surface which drives a return flow......Forcing by steep regular water waves on a vertical circular cylinder at finite depth was investigated numerically by solving the two-phase incompressible Navier–Stokes equations. Consistently with potential flow theory, boundary layer effects were neglected at the sea bed and at the cylinder...... at the back of the cylinder following the passage of the wave crest. The numerical computations were further analysed in the frequency domain. For a representative example, the secondary load cycle was found to be associated with frequencies above the fifth- and sixth-harmonic force component. For the third...

  3. Anisotropic wave-equation traveltime and waveform inversion

    KAUST Repository

    Feng, Shihang

    2016-09-06

    The wave-equation traveltime and waveform inversion (WTW) methodology is developed to invert for anisotropic parameters in a vertical transverse isotropic (VTI) meidum. The simultaneous inversion of anisotropic parameters v0, ε and δ is initially performed using the wave-equation traveltime inversion (WT) method. The WT tomograms are then used as starting background models for VTI full waveform inversion. Preliminary numerical tests on synthetic data demonstrate the feasibility of this method for multi-parameter inversion.

  4. On the Generalized Maxwell Equations and Their Prediction of Electroscalar Wave

    Directory of Open Access Journals (Sweden)

    Arbab A. I.

    2009-04-01

    Full Text Available We have formulated the basic laws of electromagnetic theory in quaternion form. The formalism shows that Maxwell equations and Lorentz force are derivable from just one quaternion equation that only requires the Lorentz gauge. We proposed a quaternion form of the continuity equation from which we have derived the ordinary continuity equation. We introduce new transformations that produces a scalar wave and generalize the continuity equation to a set of three equations. These equations imply that both current and density are waves. Moreover, we have shown that the current can not cir- culate around a point emanating from it. Maxwell equations are invariant under these transformations. An electroscalar wave propagating with speed of light is derived upon requiring the invariance of the energy conservation equation under the new transforma- tions. The electroscalar wave function is found to be proportional to the electric field component along the charged particle motion. This scalar wave exists with or without considering the Lorentz gauge. We have shown that the electromagnetic fields travel with speed of light in the presence or absence of free charges.

  5. Wave equations for pulse propagation

    International Nuclear Information System (INIS)

    Shore, B.W.

    1987-01-01

    Theoretical discussions of the propagation of pulses of laser radiation through atomic or molecular vapor rely on a number of traditional approximations for idealizing the radiation and the molecules, and for quantifying their mutual interaction by various equations of propagation (for the radiation) and excitation (for the molecules). In treating short-pulse phenomena it is essential to consider coherent excitation phenomena of the sort that is manifest in Rabi oscillations of atomic or molecular populations. Such processes are not adequately treated by rate equations for excitation nor by rate equations for radiation. As part of a more comprehensive treatment of the coupled equations that describe propagation of short pulses, this memo presents background discussion of the equations that describe the field. This memo discusses the origin, in Maxwell's equations, of the wave equation used in the description of pulse propagation. It notes the separation into lamellar and solenoidal (or longitudinal and transverse) and positive and negative frequency parts. It mentions the possibility of separating the polarization field into linear and nonlinear parts, in order to define a susceptibility or index of refraction and, from these, a phase and group velocity. The memo discusses various ways of characterizing the polarization characteristics of plane waves, that is, of parameterizing a transverse unit vector, such as the Jones vector, the Stokes vector, and the Poincare sphere. It discusses the connection between macroscopically defined quantities, such as the intensity or, more generally, the Stokes parameters, and microscopic field amplitudes. The material presented here is a portion of a more extensive treatment of propagation to be presented separately. The equations presented here have been described in various books and articles. They are collected here as a summary and review of theory needed when treating pulse propagation

  6. Local energy decay for linear wave equations with variable coefficients

    Science.gov (United States)

    Ikehata, Ryo

    2005-06-01

    A uniform local energy decay result is derived to the linear wave equation with spatial variable coefficients. We deal with this equation in an exterior domain with a star-shaped complement. Our advantage is that we do not assume any compactness of the support on the initial data, and its proof is quite simple. This generalizes a previous famous result due to Morawetz [The decay of solutions of the exterior initial-boundary value problem for the wave equation, Comm. Pure Appl. Math. 14 (1961) 561-568]. In order to prove local energy decay, we mainly apply two types of ideas due to Ikehata-Matsuyama [L2-behaviour of solutions to the linear heat and wave equations in exterior domains, Sci. Math. Japon. 55 (2002) 33-42] and Todorova-Yordanov [Critical exponent for a nonlinear wave equation with damping, J. Differential Equations 174 (2001) 464-489].

  7. Topological horseshoes in travelling waves of discretized nonlinear wave equations

    International Nuclear Information System (INIS)

    Chen, Yi-Chiuan; Chen, Shyan-Shiou; Yuan, Juan-Ming

    2014-01-01

    Applying the concept of anti-integrable limit to coupled map lattices originated from space-time discretized nonlinear wave equations, we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions. In particular, the coupled map lattices display spatio-temporal chaos on the horseshoes

  8. Topological horseshoes in travelling waves of discretized nonlinear wave equations

    Energy Technology Data Exchange (ETDEWEB)

    Chen, Yi-Chiuan, E-mail: YCChen@math.sinica.edu.tw [Institute of Mathematics, Academia Sinica, Taipei 10617, Taiwan (China); Chen, Shyan-Shiou, E-mail: sschen@ntnu.edu.tw [Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan (China); Yuan, Juan-Ming, E-mail: jmyuan@pu.edu.tw [Department of Financial and Computational Mathematics, Providence University, Shalu, Taichung 43301, Taiwan (China)

    2014-04-15

    Applying the concept of anti-integrable limit to coupled map lattices originated from space-time discretized nonlinear wave equations, we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions. In particular, the coupled map lattices display spatio-temporal chaos on the horseshoes.

  9. Gravitational wave detection by bounded cold electronic plasma in a long pipe

    OpenAIRE

    Jalili, O.; Rouhani, S.; Takook, M. V.

    2013-01-01

    We intend to propose an experimental sketch to detect gravitational waves (GW) directly, using an cold electronic plasma in a long pipe. By considering an cold electronic plasma in a long pipe, the Maxwell equations in 3+1 formalism will be invoked to relate gravitational waves to the perturbations of plasma particles. It will be shown that the impact of GW on cold electronic plasma causes disturbances on the paths of the electrons. Those electrons that absorb energy from GW will pass through...

  10. Wave equations on anti self dual (ASD) manifolds

    Science.gov (United States)

    Bashingwa, Jean-Juste; Kara, A. H.

    2017-11-01

    In this paper, we study and perform analyses of the wave equation on some manifolds with non diagonal metric g_{ij} which are of neutral signatures. These include the invariance properties, variational symmetries and conservation laws. In the recent past, wave equations on the standard (space time) Lorentzian manifolds have been performed but not on the manifolds from metrics of neutral signatures.

  11. Skeletonized wave-equation inversion for Q

    KAUST Repository

    Dutta, Gaurav

    2016-09-06

    A wave-equation gradient optimization method is presented that inverts for the subsurface Q distribution by minimizing a skeletonized misfit function ε. Here, ε is the sum of the squared differences between the observed and the predicted peak/centroid frequency shifts of the early-arrivals. The gradient is computed by migrating the observed traces weighted by the frequency-shift residuals. The background Q model is perturbed until the predicted and the observed traces have the same peak frequencies or the same centroid frequencies. Numerical tests show that an improved accuracy of the inverted Q model by wave-equation Q tomography (WQ) leads to a noticeable improvement in the migration image quality.

  12. Skeletonized wave-equation inversion for Q

    KAUST Repository

    Dutta, Gaurav; Schuster, Gerard T.

    2016-01-01

    A wave-equation gradient optimization method is presented that inverts for the subsurface Q distribution by minimizing a skeletonized misfit function ε. Here, ε is the sum of the squared differences between the observed and the predicted peak/centroid frequency shifts of the early-arrivals. The gradient is computed by migrating the observed traces weighted by the frequency-shift residuals. The background Q model is perturbed until the predicted and the observed traces have the same peak frequencies or the same centroid frequencies. Numerical tests show that an improved accuracy of the inverted Q model by wave-equation Q tomography (WQ) leads to a noticeable improvement in the migration image quality.

  13. Elliptic and solitary wave solutions for Bogoyavlenskii equations system, couple Boiti-Leon-Pempinelli equations system and Time-fractional Cahn-Allen equation

    Directory of Open Access Journals (Sweden)

    Mostafa M.A. Khater

    Full Text Available In this article and for the first time, we introduce and describe Khater method which is a new technique for solving nonlinear partial differential equations (PDEs.. We apply this method for each of the following models Bogoyavlenskii equation, couple Boiti-Leon-Pempinelli system and Time-fractional Cahn-Allen equation. Khater method is very powerful, Effective, felicitous and fabulous method to get exact and solitary wave solution of (PDEs.. Not only just like that but it considers too one of the general methods for solving that kind of equations since it involves some methods as we will see in our discuss of the results. We make a comparison between the results of this new method and another method. Keywords: Bogoyavlenskii equations system, Couple Boiti-Leon-Pempinelli equations system, Time-fractional Cahn-Allen equation, Khater method, Traveling wave solutions, Solitary wave solutions

  14. Periodic and solitary-wave solutions of the Degasperis-Procesi equation

    International Nuclear Information System (INIS)

    Vakhnenko, V.O.; Parkes, E.J.

    2004-01-01

    Travelling-wave solutions of the Degasperis-Procesi equation are investigated. The solutions are characterized by two parameters. For propagation in the positive x-direction, hump-like, inverted loop-like and coshoidal periodic-wave solutions are found; hump-like, inverted loop-like and peakon solitary-wave solutions are obtained as well. For propagation in the negative x-direction, there are solutions which are just the mirror image in the x-axis of the aforementioned solutions. A transformed version of the Degasperis-Procesi equation, which is a generalization of the Vakhnenko equation, is also considered. For propagation in the positive x-direction, hump-like, loop-like, inverted loop-like, bell-like and coshoidal periodic-wave solutions are found; loop-like, inverted loop-like and kink-like solitary-wave solutions are obtained as well. For propagation in the negative x-direction, well-like and inverted coshoidal periodic-wave solutions are found; well-like and inverted peakon solitary-wave solutions are obtained as well. In an appropriate limit, the previously known solutions of the Vakhnenko equation are recovered

  15. Initial-value problem for the Gardner equation applied to nonlinear internal waves

    Science.gov (United States)

    Rouvinskaya, Ekaterina; Kurkina, Oxana; Kurkin, Andrey; Talipova, Tatiana; Pelinovsky, Efim

    2017-04-01

    solitons (family with positive polarity, and family with negative polarity bounded below by the amplitude of 2) and two-parametric family of breathers (oscillatory wave packets). In this case varying amplitude and width of bell-shaped initial impulse leads to plenty of different evolutionary scenarios with the generation of solitary waves, breathers, solibores and nonlinear Airy wave in their various combinations. Statistical analysis of the wave field in time shows almost permanent substantial exceedance of the level of the significant wave height in some position in spatial coordinate. Evolution of Fourier spectrum of the wave field is also analyzed, and its behavior after a long time of initial wave evolution demonstrates the power asymptotic for small wave numbers and exponential asymptotic for large wave numbers. The presented results of research are obtained with the support of the grant of the President of the Russian Federation for state support of the young Russian scientists - Candidates of Sciences (MK-5208.2016.5) and Russian Foundation for Basic Research grant 16-05-00049. References: Grimshaw R., Pelinovsky D., Pelinovsky E and Slunyaev A. Generation of large-amplitude solitons in the extended Korteweg-de Vries equation // Chaos, 2002. - V.12. - No 4. - 1070-1076. Grimshaw, R., Slunyaev, A., and Pelinovsky, E. Generation of solitons and breathers in the extended Korteweg-de Vries equation with positive cubic nonlinearity //Chaos, 2010. - vol. 20.-013102. Kurkina O.E., Kurkin A.A., Soomere T., Pelinovsky E.N., Rouvinskaya E.A. Higher-order (2+4) Korteweg-de Vries - like equation for interfacial waves in a symmetric three-layer fluid // Physics of Fluids, 2011. - Volume 23. - Issue 11. - p.116602--1--13. Kurkina O., Rouvinskaya E., Talipova T., Kurkin A., Pelinovsky E. Nonlinear disintegration of sine wave in the framework of the Gardner equation // Physica D: Nonlinear Phenomena, 2015. - doi:10.1016/j.physd.2015.12.007. Pelinovsky E., Polukhina O., Slunyaev A

  16. New exact travelling wave solutions of bidirectional wave equations

    Indian Academy of Sciences (India)

    Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea. ∗ ... exact travelling wave solutions of system (1) using the modified tanh–coth function method ... The ordinary differential equation is then integrated.

  17. New traveling wave solutions to AKNS and SKdV equations

    International Nuclear Information System (INIS)

    Ozer, Teoman

    2009-01-01

    We analyze the traveling wave solutions of Ablowitz-Kaup-Newell-Segur (AKNS) and Schwarz-Korteweg-de Vries (SKdV) equations. As the solution method for differential equations we consider the improved tanh approach. This approach provides to transform the partial differential equation into the ordinary differential equation and then obtain the new families of exact solutions based on the solutions of the Riccati equation. The different values of the coefficients of the Riccati equation allow us to obtain new type of traveling wave solutions to AKNS and SKdV equations.

  18. Eulerian Simulation of Acoustic Waves Over Long Range in Realistic Environments

    Science.gov (United States)

    Chitta, Subhashini; Steinhoff, John

    2015-11-01

    In this paper, we describe a new method for computation of long-range acoustics. The approach is a hybrid of near and far-field methods, and is unique in its Eulerian treatment of the far-field propagation. The near-field generated by any existing method to project an acoustic solution onto a spherical surface that surrounds a source. The acoustic field on this source surface is then extended to an arbitrarily large distance in an inhomogeneous far-field. This would normally require an Eulerian solution of the wave equation. However, conventional Eulerian methods have prohibitive grid requirements. This problem is overcome by using a new method, ``Wave Confinement'' (WC) that propagates wave-identifying phase fronts as nonlinear solitary waves that live on grid indefinitely. This involves modification of wave equation by the addition of a nonlinear term without changing the basic conservation properties of the equation. These solitary waves can then be used to ``carry'' the essential integrals of the acoustic wave. For example, arrival time, centroid position and other properties that are invariant as the wave passes a grid point. Because of this property the grid can be made as coarse as necessary, consistent with overall accuracy to resolve atmospheric/ground variations. This work is being funded by the U.S. Army under a Small Business Innovation Research (SBIR) program (contract number: # W911W6-12-C-0036). The authors would like to thank Dr. Frank Caradonna and Dr. Ben W. Sim for this support.

  19. Short-time regularity assessment of fibrillatory waves from the surface ECG in atrial fibrillation

    International Nuclear Information System (INIS)

    Alcaraz, Raúl; Martínez, Arturo; Hornero, Fernando; Rieta, José J

    2012-01-01

    This paper proposes the first non-invasive method for direct and short-time regularity quantification of atrial fibrillatory (f) waves from the surface ECG in atrial fibrillation (AF). Regularity is estimated by computing individual morphological variations among f waves, which are delineated and extracted from the atrial activity (AA) signal, making use of an adaptive signed correlation index. The algorithm was tested on real AF surface recordings in order to discriminate atrial signals with different organization degrees, providing a notably higher global accuracy (90.3%) than the two non-invasive AF organization estimates defined to date: the dominant atrial frequency (70.5%) and sample entropy (76.1%). Furthermore, due to its ability to assess AA regularity wave to wave, the proposed method is also able to pursue AF organization time course more precisely than the aforementioned indices. As a consequence, this work opens a new perspective in the non-invasive analysis of AF, such as the individualized study of each f wave, that could improve the understanding of AF mechanisms and become useful for its clinical treatment. (paper)

  20. Spontaneous long-range calcium waves in developing butterfly wings.

    Science.gov (United States)

    Ohno, Yoshikazu; Otaki, Joji M

    2015-03-25

    Butterfly wing color patterns emerge as the result of a regular arrangement of scales produced by epithelial scale cells at the pupal stage. These color patterns and scale arrangements are coordinated throughout the wing. However, the mechanism by which the development of scale cells is controlled across the entire wing remains elusive. In the present study, we used pupal wings of the blue pansy butterfly, Junonia orithya, which has distinct eyespots, to examine the possible involvement of Ca(2+) waves in wing development. Here, we demonstrate that the developing pupal wing tissue of the blue pansy butterfly displayed spontaneous low-frequency Ca(2+) waves in vivo that propagated slowly over long distances. Some waves appeared to be released from the immediate peripheries of the prospective eyespot and discal spot, though it was often difficult to identify the specific origins of these waves. Physical damage, which is known to induce ectopic eyespots, led to the radiation of Ca(2+) waves from the immediate periphery of the damaged site. Thapsigargin, which is a specific inhibitor of Ca(2+)-ATPases in the endoplasmic reticulum, induced an acute increase in cytoplasmic Ca(2+) levels and halted the spontaneous Ca(2+) waves. Additionally, thapsigargin-treated wings showed incomplete scale development as well as other scale and color pattern abnormalities. We identified a novel form of Ca(2+) waves, spontaneous low-frequency slow waves, which travel over exceptionally long distances. Our results suggest that spontaneous Ca(2+) waves play a critical role in the coordinated development of scale arrangements and possibly in color pattern formation in butterflies.

  1. The time dependent Schrodinger equation revisited I: quantum field and classical Hamilton-Jacobi routes to Schrodinger's wave equation

    International Nuclear Information System (INIS)

    Scully, M O

    2008-01-01

    The time dependent Schrodinger equation is frequently 'derived' by postulating the energy E → i h-bar (∂/∂t) and momentum p-vector → ( h-bar /i)∇ operator relations. In the present paper we review the quantum field theoretic route to the Schrodinger wave equation which treats time and space as parameters, not operators. Furthermore, we recall that a classical (nonlinear) wave equation can be derived from the classical action via Hamiltonian-Jacobi theory. By requiring the wave equation to be linear we again arrive at the Schrodinger equation, without postulating operator relations. The underlying philosophy is operational: namely 'a particle is what a particle detector detects.' This leads us to a useful physical picture combining the wave (field) and particle paradigms which points the way to the time-dependent Schrodinger equation

  2. Dynamic equations for gauge-invariant wave functions

    International Nuclear Information System (INIS)

    Kapshaj, V.N.; Skachkov, N.B.; Solovtsov, I.L.

    1984-01-01

    The Bethe-Salpeter and quasipotential dynamic equations for wave functions of relative quark motion, have been derived. Wave functions are determined by the gauge invariant method. The V.A. Fock gauge condition is used in the construction. Despite the transl tional noninvariance of the gauge condition the standard separation of variables has been obtained and wave function doesn't contain gauge exponents

  3. Reflected rarefactions, double regular reflection, and mach waves in aluminum and beryllium

    International Nuclear Information System (INIS)

    Neal, T.

    1975-01-01

    A number of shock techniques which can be used to obtain high-pressure equation-of-state information between the principal Hugoniot and the principal adiabat are illustrated. A rarefaction wave in aluminum shocked to 27.7 GPa [277 kbar] is examined with radiographic techniques and the bulk sound speed is determined. The two stage compression which occurs in a double shock may be attained by colliding two shocks and observing regular reflection. A radiographic method which uses this phenomenon to measure a three-stage compression of aluminum to a density of 4.7 Mg/m 3 and beryllium to a density of 3.1 Mg/m 3 is presented. The results of a Mach reflection experiment in aluminum are found to disagree substantially with the simple three-shock model. A modified model, consistent with observations, is discussed. In all cases the Gruneisen parameter is determined. (U.S.)

  4. The propagation of travelling waves for stochastic generalized KPP equations

    International Nuclear Information System (INIS)

    Elworthy, K.D.; Zhao, H.Z.

    1993-09-01

    We study the existence and propagation of approximate travelling waves of generalized KPP equations with seasonal multiplicative white noise perturbations of Ito type. Three regimes of perturbation are considered: weak, milk, and strong. We show that weak perturbations have little effect on the wave like solutions of the unperturbed equations while strong perturbations essentially destroy the wave and force the solutions to die down. For mild perturbations we show that there is a residual wave form but propagating at a different speed to that of the unperturbed equation. In the appendix J.G. Gaines illustrates these different regimes by computer simulations. (author). 27 refs, 13 figs

  5. Computational study on full-wave inversion based on the elastic wave-equation; Dansei hado hoteishiki full wave inversion no model keisan ni yoru kento

    Energy Technology Data Exchange (ETDEWEB)

    Uesaka, S [Kyoto University, Kyoto (Japan). Faculty of Engineering; Watanabe, T; Sassa, K [Kyoto University, Kyoto (Japan)

    1997-05-27

    Algorithm is constructed and a program developed for a full-wave inversion (FWI) method utilizing the elastic wave equation in seismic exploration. The FWI method is a method for obtaining a physical property distribution using the whole observed waveforms as the data. It is capable of high resolution which is several times smaller than the wavelength since it can handle such phenomena as wave reflection and dispersion. The method for determining the P-wave velocity structure by use of the acoustic wave equation does not provide information about the S-wave velocity since it does not consider S-waves or converted waves. In an analysis using the elastic wave equation, on the other hand, not only P-wave data but also S-wave data can be utilized. In this report, under such circumstances, an inverse analysis algorithm is constructed on the basis of the elastic wave equation, and a basic program is developed. On the basis of the methods of Mora and of Luo and Schuster, the correction factors for P-wave and S-wave velocities are formulated directly from the elastic wave equation. Computations are performed and the effects of the hypocenter frequency and vibration transmission direction are examined. 6 refs., 8 figs.

  6. Nonlinear electrostatic wave equations for magnetized plasmas - II

    DEFF Research Database (Denmark)

    Dysthe, K. B.; Mjølhus, E.; Pécseli, H. L.

    1985-01-01

    For pt.I see ibid., vol.26, p.443-7 (1984). The problem of extending the high frequency part of the Zakharov equations for nonlinear electrostatic waves to magnetized plasmas, is considered. Weak electromagnetic and thermal effects are retained on an equal footing. Direction dependent (electrosta......For pt.I see ibid., vol.26, p.443-7 (1984). The problem of extending the high frequency part of the Zakharov equations for nonlinear electrostatic waves to magnetized plasmas, is considered. Weak electromagnetic and thermal effects are retained on an equal footing. Direction dependent...... (electrostatic) cut-off implies that various cases must be considered separately, leading to equations with rather different properties. Various equations encountered previously in the literature are recovered as limiting cases....

  7. Relativistic covariant wave equations and acausality in external fields

    International Nuclear Information System (INIS)

    Pijlgroms, R.B.J.

    1980-01-01

    The author considers linear, finite dimensional, first order relativistic wave equations: (βsup(μ)ideltasub(μ)-β)PSI(x) = 0 with βsup(μ) and β constant matrices. Firstly , the question of the relativistic covariance conditions on these equations is considered. Then the theory of these equations with β non-singular is summarized. Theories with βsup(μ), β square matrices and β singular are also discussed. Non-square systems of covariant relativistic wave equations for arbitrary spin > 1 are then considered. Finally, the interaction with external fields and the acausality problem are discussed. (G.T.H.)

  8. Hölder Regularity of the 2D Dual Semigeostrophic Equations via Analysis of Linearized Monge-Ampère Equations

    Science.gov (United States)

    Le, Nam Q.

    2018-05-01

    We obtain the Hölder regularity of time derivative of solutions to the dual semigeostrophic equations in two dimensions when the initial potential density is bounded away from zero and infinity. Our main tool is an interior Hölder estimate in two dimensions for an inhomogeneous linearized Monge-Ampère equation with right hand side being the divergence of a bounded vector field. As a further application of our Hölder estimate, we prove the Hölder regularity of the polar factorization for time-dependent maps in two dimensions with densities bounded away from zero and infinity. Our applications improve previous work by G. Loeper who considered the cases of densities sufficiently close to a positive constant.

  9. Multiple attenuation to reflection seismic data using Radon filter and Wave Equation Multiple Rejection (WEMR) method

    Energy Technology Data Exchange (ETDEWEB)

    Erlangga, Mokhammad Puput [Geophysical Engineering, Institut Teknologi Bandung, Ganesha Street no.10 Basic Science B Buliding fl.2-3 Bandung, 40132, West Java Indonesia puput.erlangga@gmail.com (Indonesia)

    2015-04-16

    Separation between signal and noise, incoherent or coherent, is important in seismic data processing. Although we have processed the seismic data, the coherent noise is still mixing with the primary signal. Multiple reflections are a kind of coherent noise. In this research, we processed seismic data to attenuate multiple reflections in the both synthetic and real seismic data of Mentawai. There are several methods to attenuate multiple reflection, one of them is Radon filter method that discriminates between primary reflection and multiple reflection in the τ-p domain based on move out difference between primary reflection and multiple reflection. However, in case where the move out difference is too small, the Radon filter method is not enough to attenuate the multiple reflections. The Radon filter also produces the artifacts on the gathers data. Except the Radon filter method, we also use the Wave Equation Multiple Elimination (WEMR) method to attenuate the long period multiple reflection. The WEMR method can attenuate the long period multiple reflection based on wave equation inversion. Refer to the inversion of wave equation and the magnitude of the seismic wave amplitude that observed on the free surface, we get the water bottom reflectivity which is used to eliminate the multiple reflections. The WEMR method does not depend on the move out difference to attenuate the long period multiple reflection. Therefore, the WEMR method can be applied to the seismic data which has small move out difference as the Mentawai seismic data. The small move out difference on the Mentawai seismic data is caused by the restrictiveness of far offset, which is only 705 meter. We compared the real free multiple stacking data after processing with Radon filter and WEMR process. The conclusion is the WEMR method can more attenuate the long period multiple reflection than the Radon filter method on the real (Mentawai) seismic data.

  10. Travelling wave solutions of the generalized Benjamin-Bona-Mahony equation

    International Nuclear Information System (INIS)

    Estevez, P.G.; Kuru, S.; Negro, J.; Nieto, L.M.

    2009-01-01

    A class of particular travelling wave solutions of the generalized Benjamin-Bona-Mahony equation is studied systematically using the factorization technique. Then, the general travelling wave solutions of Benjamin-Bona-Mahony equation, and of its modified version, are also recovered.

  11. Semiclassical regularization of Vlasov equations and wavepackets for nonlinear Schrödinger equations

    Science.gov (United States)

    Athanassoulis, Agissilaos

    2018-03-01

    We consider the semiclassical limit of nonlinear Schrödinger equations with initial data that are well localized in both position and momentum (non-parametric wavepackets). We recover the Wigner measure (WM) of the problem, a macroscopic phase-space density which controls the propagation of the physical observables such as mass, energy and momentum. WMs have been used to create effective models for wave propagation in: random media, quantum molecular dynamics, mean field limits, and the propagation of electrons in graphene. In nonlinear settings, the Vlasov-type equations obtained for the WM are often ill-posed on the physically interesting spaces of initial data. In this paper we are able to select the measure-valued solution of the 1  +  1 dimensional Vlasov-Poisson equation which correctly captures the semiclassical limit, thus finally resolving the non-uniqueness in the seminal result of Zhang et al (2012 Comm. Pure Appl. Math. 55 582-632). The same approach is also applied to the Vlasov-Dirac-Benney equation with small wavepacket initial data, extending several known results.

  12. On Regularly Varying and History-Dependent Convergence Rates of Solutions of a Volterra Equation with Infinite Memory

    Directory of Open Access Journals (Sweden)

    Appleby JohnAD

    2010-01-01

    Full Text Available We consider the rate of convergence to equilibrium of Volterra integrodifferential equations with infinite memory. We show that if the kernel of Volterra operator is regularly varying at infinity, and the initial history is regularly varying at minus infinity, then the rate of convergence to the equilibrium is regularly varying at infinity, and the exact pointwise rate of convergence can be determined in terms of the rate of decay of the kernel and the rate of growth of the initial history. The result is considered both for a linear Volterra integrodifferential equation as well as for the delay logistic equation from population biology.

  13. Reduction of the equation for lower hybrid waves in a plasma to a nonlinear Schroedinger equation

    Science.gov (United States)

    Karney, C. F. F.

    1977-01-01

    Equations describing the nonlinear propagation of waves in an anisotropic plasma are rarely exactly soluble. However it is often possible to make approximations that reduce the exact equations into a simpler equation. The use of MACSYMA to make such approximations, and so reduce the equation describing lower hybrid waves into the nonlinear Schrodinger equation which is soluble by the inverse scattering method is demonstrated. MACSYMA is used at several stages in the calculation only because there is a natural division between calculations that are easiest done by hand, and those that are easiest done by machine.

  14. Quantum-Wave Equation and Heisenberg Inequalities of Covariant Quantum Gravity

    Directory of Open Access Journals (Sweden)

    Claudio Cremaschini

    2017-07-01

    Full Text Available Key aspects of the manifestly-covariant theory of quantum gravity (Cremaschini and Tessarotto 2015–2017 are investigated. These refer, first, to the establishment of the four-scalar, manifestly-covariant evolution quantum wave equation, denoted as covariant quantum gravity (CQG wave equation, which advances the quantum state ψ associated with a prescribed background space-time. In this paper, the CQG-wave equation is proved to follow at once by means of a Hamilton–Jacobi quantization of the classical variational tensor field g ≡ g μ ν and its conjugate momentum, referred to as (canonical g-quantization. The same equation is also shown to be variational and to follow from a synchronous variational principle identified here with the quantum Hamilton variational principle. The corresponding quantum hydrodynamic equations are then obtained upon introducing the Madelung representation for ψ , which provides an equivalent statistical interpretation of the CQG-wave equation. Finally, the quantum state ψ is proven to fulfill generalized Heisenberg inequalities, relating the statistical measurement errors of quantum observables. These are shown to be represented in terms of the standard deviations of the metric tensor g ≡ g μ ν and its quantum conjugate momentum operator.

  15. Characteristics of phase-averaged equations for modulated wave groups

    NARCIS (Netherlands)

    Klopman, G.; Petit, H.A.H.; Battjes, J.A.

    2000-01-01

    The project concerns the influence of long waves on coastal morphology. The modelling of the combined motion of the long waves and short waves in the horizontal plane is done by phase-averaging over the short wave motion and using intra-wave modelling for the long waves, see e.g. Roelvink (1993).

  16. Unified formulation of radiation conditions for the wave equation

    DEFF Research Database (Denmark)

    Krenk, Steen

    2002-01-01

    A family of radiation conditions for the wave equation is derived by truncating a rational function approxiamtion of the corresponding plane wave representation, and it is demonstrated how these boundary conditions can be formulated in terms of fictitious surface densities, governed by second......-order wave equations on the radiating surface. Several well-established radiation boundary conditions appear as special cases, corresponding to different choice of the coefficients in the rational approximation. The relation between these choices is established, and an explicit formulation in terms...

  17. Three-dimensional wave-induced current model equations and radiation stresses

    Science.gov (United States)

    Xia, Hua-yong

    2017-08-01

    After the approach by Mellor (2003, 2008), the present paper reports on a repeated effort to derive the equations for three-dimensional wave-induced current. Via the vertical momentum equation and a proper coordinate transformation, the phase-averaged wave dynamic pressure is well treated, and a continuous and depth-dependent radiation stress tensor, rather than the controversial delta Dirac function at the surface shown in Mellor (2008), is provided. Besides, a phase-averaged vertical momentum flux over a sloping bottom is introduced. All the inconsistencies in Mellor (2003, 2008), pointed out by Ardhuin et al. (2008) and Bennis and Ardhuin (2011), are overcome in the presently revised equations. In a test case with a sloping sea bed, as shown in Ardhuin et al. (2008), the wave-driving forces derived in the present equations are in good balance, and no spurious vertical circulation occurs outside the surf zone, indicating that Airy's wave theory and the approach of Mellor (2003, 2008) are applicable for the derivation of the wave-induced current model.

  18. Nonlinear wave runup in long bays and firths: Samoa 2009 and Tohoku 2011 tsunamis

    Science.gov (United States)

    Didenkulova, I.; Pelinovsky, E.

    2012-04-01

    Last catastrophic tsunami events in Samoa on 29 September 2009 and in Japan on 11 March 2011 demonstrated that tsunami may experience abnormal amplification in long bays and firths and result in an unexpectedly high wave runup. The capital city Pago Pago, which is located at the toe of a narrow 4-km-long bay and represents the most characteristic example of a long and narrow bay, was considerably damaged during Samoa 2009 tsunami (destroyed infrastructures, boats and shipping containers carried inland into commercial areas, etc.) The runup height there reached 8 m over an inundation of 538 m at its toe, while the tsunami wave height measured by the tide-gauge at the entrance of the bay was at most 3 m. The same situation was observed during catastrophic Tohoku tsunami in Japan, which coast contains numerous long bays and firths, which experienced the highest wave runup and the strongest amplification. Such examples are villages: Ofunato, Ryori Bay, where the wave runup reached 30 m high, and Onagawa, where the wave amplified up to 17 m. Here we study the nonlinear dynamics of tsunami waves in an inclined U-shaped bay. Nonlinear shallow water equations can in this case be written in 1D form and solved analytically with the use of the hodograph transformation. This approach generalizes the well-known Carrier-Greenspan transformation for long wave runup on a plane beach. In the case of an inclined U-shaped bay it leads to the associated generalized wave equation for symmetrical wave in fractal space. In the special case of the channel of parabolic cross-section it is a spherical symmetrical linear wave equation. As a result, the solution of the Cauchy problem can be expressed in terms of elementary functions and has a simple form (with respect to analysis) for any kind of initial conditions. Wave regimes associated with various localized initial conditions, corresponding to problems of evolution and runup of tsunami, are considered and analyzed. Special attention is

  19. Some Further Results on Traveling Wave Solutions for the ZK-BBM( Equations

    Directory of Open Access Journals (Sweden)

    Shaoyong Li

    2013-01-01

    Full Text Available We investigate the traveling wave solutions for the ZK-BBM( equations by using bifurcation method of dynamical systems. Firstly, for ZK-BBM(2, 2 equation, we obtain peakon wave, periodic peakon wave, and smooth periodic wave solutions and point out that the peakon wave is the limit form of the periodic peakon wave. Secondly, for ZK-BBM(3, 2 equation, we obtain some elliptic function solutions which include periodic blow-up and periodic wave. Furthermore, from the limit forms of the elliptic function solutions, we obtain some trigonometric and hyperbolic function solutions which include periodic blow-up, blow-up, and smooth solitary wave. We also show that our work extends some previous results.

  20. Conditional Stability of Solitary-Wave Solutions for Generalized Compound KdV Equation and Generalized Compound KdV-Burgers Equation

    International Nuclear Information System (INIS)

    Zhang Weiguo; Dong Chunyan; Fan Engui

    2006-01-01

    In this paper, we discuss conditional stability of solitary-wave solutions in the sense of Liapunov for the generalized compound KdV equation and the generalized compound KdV-Burgers equations. Linear stability of the exact solitary-wave solutions is proved for the above two types of equations when the small disturbance of travelling wave form satisfies some special conditions.

  1. Imaging of the internal structure of comet 67P/Churyumov-Gerasimenko from radiotomography CONSERT Data (Rosetta Mission) through a full 3D regularized inversion of the Helmholtz equations on functional spaces

    Science.gov (United States)

    Barriot, Jean-Pierre; Serafini, Jonathan; Sichoix, Lydie; Benna, Mehdi; Kofman, Wlodek; Herique, Alain

    We investigate the inverse problem of imaging the internal structure of comet 67P/ Churyumov-Gerasimenko from radiotomography CONSERT data by using a coupled regularized inversion of the Helmholtz equations. A first set of Helmholtz equations, written w.r.t a basis of 3D Hankel functions describes the wave propagation outside the comet at large distances, a second set of Helmholtz equations, written w.r.t. a basis of 3D Zernike functions describes the wave propagation throughout the comet with avariable permittivity. Both sets are connected by continuity equations over a sphere that surrounds the comet. This approach, derived from GPS water vapor tomography of the atmosphere,will permit a full 3D inversion of the internal structure of the comet, contrary to traditional approaches that use a discretization of space at a fraction of the radiowave wavelength.

  2. Generalised master equations for wave equation separation in a Kerr or Kerr-Newman black hole background

    International Nuclear Information System (INIS)

    Carter, B.; McLenaghan, R.G.

    1982-01-01

    It is shown how previous general formulae for the separated radial and angular parts of the massive, charged scalar (Klein, Gordon) wave equation on one hand, and of the zero mass, neutral, but higher spin (neutrino, electromagnetic and gravitational) wave equations on the other hand may be combined in a more general formula which also covers the case of the full massive charged Dirac equation in a Kerr or Kerr-Newman background space. (Auth.)

  3. Robust Imaging Methodology for Challenging Environments: Wave Equation Dispersion Inversion of Surface Waves

    KAUST Repository

    Li, Jing; Schuster, Gerard T.; Zeng, Zhaofa

    2017-01-01

    A robust imaging technology is reviewed that provide subsurface information in challenging environments: wave-equation dispersion inversion (WD) of surface waves for the shear velocity model. We demonstrate the benefits and liabilities of the method

  4. Closed form solutions of two time fractional nonlinear wave equations

    Directory of Open Access Journals (Sweden)

    M. Ali Akbar

    2018-06-01

    Full Text Available In this article, we investigate the exact traveling wave solutions of two nonlinear time fractional wave equations. The fractional derivatives are described in the sense of conformable fractional derivatives. In addition, the traveling wave solutions are accomplished in the form of hyperbolic, trigonometric, and rational functions involving free parameters. To investigate such types of solutions, we implement the new generalized (G′/G-expansion method. The extracted solutions are reliable, useful and suitable to comprehend the optimal control problems, chaotic vibrations, global and local bifurcations and resonances, furthermore, fission and fusion phenomena occur in solitons, the relativistic energy-momentum relation, scalar electrodynamics, quantum relativistic one-particle theory, electromagnetic interactions etc. The results reveal that the method is very fruitful and convenient for exploring nonlinear differential equations of fractional order treated in theoretical physics. Keywords: Traveling wave solution, Soliton, Generalized (G′/G-expansion method, Time fractional Duffing equation, Time fractional Riccati equation

  5. Inverse Schroedinger equation and the exact wave function

    International Nuclear Information System (INIS)

    Nakatsuji, Hiroshi

    2002-01-01

    Using the inverse of the Hamiltonian, we introduce the inverse Schroedinger equation (ISE) that is equivalent to the ordinary Schroedinger equation (SE). The ISE has the variational principle and the H-square group of equations as the SE has. When we use a positive Hamiltonian, shifting the energy origin, the inverse energy becomes monotonic and we further have the inverse Ritz variational principle and cross-H-square equations. The concepts of the SE and the ISE are combined to generalize the theory for calculating the exact wave function that is a common eigenfunction of the SE and ISE. The Krylov sequence is extended to include the inverse Hamiltonian, and the complete Krylov sequence is introduced. The iterative configuration interaction (ICI) theory is generalized to cover both the SE and ISE concepts and four different computational methods of calculating the exact wave function are presented in both analytical and matrix representations. The exact wave-function theory based on the inverse Hamiltonian can be applied to systems that have singularities in the Hamiltonian. The generalized ICI theory is applied to the hydrogen atom, giving the exact solution without any singularity problem

  6. Painleve analysis for a forced Korteveg-de Vries equation arisen in fluid dynamics of internal solitary waves

    Directory of Open Access Journals (Sweden)

    Zhang Sheng

    2015-01-01

    Full Text Available In this paper, Painleve analysis is used to test the Painleve integrability of a forced variable-coefficient extended Korteveg-de Vries equation which can describe the weakly-non-linear long internal solitary waves in the fluid with continuous stratification on density. The obtained results show that the equation is integrable under certain conditions. By virtue of the truncated Painleve expansion, a pair of new exact solutions to the equation is obtained.

  7. New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod

    Directory of Open Access Journals (Sweden)

    Aly R. Seadawy

    2018-03-01

    Full Text Available This paper examines the effectiveness of an integration scheme which called the extended trial equation method (ETEM in exactly solving a well-known nonlinear equation of partial differential equations (PDEs. In this respect, the longitudinal wave equation (LWE that arises in mathematical physics with dispersion caused by the transverse Poisson’s effect in a magneto-electro-elastic (MEE circular rod, which a series of exact traveling wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of the longitudinal wave equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena of this longitudinal wave equation. Many other such types of nonlinear equations arising in non-destructive evaluation of structures made of the advanced MEE material can also be solved by this method. Keywords: Extended trial equation method, Longitudinal wave equation in a MEE circular rod, Dark solitons, Bright solitons, Solitary wave, Periodic solitary wave

  8. Kolmogorov spectra of long wavelength ion-drift waves in dusty plasmas

    International Nuclear Information System (INIS)

    Onishchenko, O.G.; Pokhotelov, O.A.; Sagdeev, R.Z.; Pavlenko, V.P.; Stenflo, L.; Shukla, P.K.; Zolotukhin, V.V.

    2002-01-01

    Weakly turbulent Kolmogorov spectra of ion-drift waves in dusty plasmas with an arbitrary ratio between the ion-drift and the Shukla-Varma frequencies are investigated. It is shown that in the long wavelength limit, when the contribution to the wave dispersion associated with the inhomogeneity of the dust component is larger than that related to the plasma inhomogeneity, the wave dispersion and the matrix interaction element coincide with those for the Rossby or the electron-drift waves described by the Charney or Hasegawa-Mima equations with an accuracy of unessential numerical coefficients. It is found that the weakly turbulent spectra related to the conservation of the wave energy are local and thus the energy flux is directed towards smaller spatial scales

  9. Limiting Behavior of Travelling Waves for the Modified Degasperis-Procesi Equation

    Directory of Open Access Journals (Sweden)

    Jiuli Yin

    2014-01-01

    Full Text Available Using an improved qualitative method which combines characteristics of several methods, we classify all travelling wave solutions of the modified Degasperis-Procesi equation in specified regions of the parametric space. Besides some popular exotic solutions including peaked waves, and looped and cusped waves, this equation also admits some very particular waves, such as fractal-like waves, double stumpons, double kinked waves, and butterfly-like waves. The last three types of solutions have not been reported in the literature. Furthermore, we give the limiting behavior of all periodic solutions as the parameters trend to some special values.

  10. Simple functional-differential equations for the bound-state wave-function components

    International Nuclear Information System (INIS)

    Kamuntavicius, G.P.

    1986-01-01

    The author presents a new method of a direct derivation of differential equations for the wave-function components of identical-particles systems. The method generates in a simple manner all the possible variants of these equations. In some cases they are the differential equations of Faddeev or Yakubovskii. It is shown that the case of the bound states allows to formulate very simple equations for the components which are equivalent to the Schroedinger equation for the complete wave function. The components with a minimal antisymmetry are defined and the corresponding equations are derived. (Auth.)

  11. Fibonacci-regularization method for solving Cauchy integral equations of the first kind

    Directory of Open Access Journals (Sweden)

    Mohammad Ali Fariborzi Araghi

    2017-09-01

    Full Text Available In this paper, a novel scheme is proposed to solve the first kind Cauchy integral equation over a finite interval. For this purpose, the regularization method is considered. Then, the collocation method with Fibonacci base function is applied to solve the obtained second kind singular integral equation. Also, the error estimate of the proposed scheme is discussed. Finally, some sample Cauchy integral equations stem from the theory of airfoils in fluid mechanics are presented and solved to illustrate the importance and applicability of the given algorithm. The tables in the examples show the efficiency of the method.

  12. Exact solitary and periodic wave solutions for a generalized nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Sun Chengfeng; Gao Hongjun

    2009-01-01

    The generalized nonlinear Schroedinger equation (GNLS) iu t + u xx + β | u | 2 u + γ | u | 4 u + iα (| u | 2 u) x + iτ(| u | 2 ) x u = 0 is studied. Using the bifurcation of travelling waves of this equation, some exact solitary wave solutions were obtained in [Wang W, Sun J,Chen G, Bifurcation, Exact solutions and nonsmooth behavior of solitary waves in the generalized nonlinear Schroedinger equation. Int J Bifucat Chaos 2005:3295-305.]. In this paper, more explicit exact solitary wave solutions and some new smooth periodic wave solutions are obtained.

  13. Long-term evolution of electron distribution function due to nonlinear resonant interaction with whistler mode waves

    Science.gov (United States)

    Artemyev, Anton V.; Neishtadt, Anatoly I.; Vasiliev, Alexei A.

    2018-04-01

    Accurately modelling and forecasting of the dynamics of the Earth's radiation belts with the available computer resources represents an important challenge that still requires significant advances in the theoretical plasma physics field of wave-particle resonant interaction. Energetic electron acceleration or scattering into the Earth's atmosphere are essentially controlled by their resonances with electromagnetic whistler mode waves. The quasi-linear diffusion equation describes well this resonant interaction for low intensity waves. During the last decade, however, spacecraft observations in the radiation belts have revealed a large number of whistler mode waves with sufficiently high intensity to interact with electrons in the nonlinear regime. A kinetic equation including such nonlinear wave-particle interactions and describing the long-term evolution of the electron distribution is the focus of the present paper. Using the Hamiltonian theory of resonant phenomena, we describe individual electron resonance with an intense coherent whistler mode wave. The derived characteristics of such a resonance are incorporated into a generalized kinetic equation which includes non-local transport in energy space. This transport is produced by resonant electron trapping and nonlinear acceleration. We describe the methods allowing the construction of nonlinear resonant terms in the kinetic equation and discuss possible applications of this equation.

  14. Wave equation of hydrogen atom

    International Nuclear Information System (INIS)

    Suwito.

    1977-01-01

    The calculation of the energy levels of the hydrogen atom using Bohr, Schroedinger and Dirac theories is reviewed. The result is compared with that obtained from infinite component wave equations theory which developed recently. The conclusion can be stated that the latter theory is better to describe the composit system than the former. (author)

  15. Stumpons and fractal-like wave solutions to the Dullin-Gottwald-Holm equation

    International Nuclear Information System (INIS)

    Yin Jiuli; Tian Lixin

    2009-01-01

    The traveling wave solutions to the Dullin-Gottwald-Holm equation (called DGH equation) are classified by an improved qualitative analysis method. Meanwhile, the influence of the parameters on the traveling wave forms is specifically considered. The equation is shown to admit more traveling wave forms solutions, especially new solutions such as stumpons and fractal-like waves are first given. We also point out that the smooth solutions can converge to non-smooth ones under certain conditions. Furthermore, the new explicit forms of peakons with period are obtained.

  16. Deterministic and stochastic evolution equations for fully dispersive and weakly nonlinear waves

    DEFF Research Database (Denmark)

    Eldeberky, Y.; Madsen, Per A.

    1999-01-01

    and stochastic formulations are solved numerically for the case of cross shore motion of unidirectional waves and the results are verified against laboratory data for wave propagation over submerged bars and over a plane slope. Outside the surf zone the two model predictions are generally in good agreement......This paper presents a new and more accurate set of deterministic evolution equations for the propagation of fully dispersive, weakly nonlinear, irregular, multidirectional waves. The equations are derived directly from the Laplace equation with leading order nonlinearity in the surface boundary...... is significantly underestimated for larger wave numbers. In the present work we correct this inconsistency. In addition to the improved deterministic formulation, we present improved stochastic evolution equations in terms of the energy spectrum and the bispectrum for multidirectional waves. The deterministic...

  17. Stability of negative solitary waves for an integrable modified Camassa-Holm equation

    International Nuclear Information System (INIS)

    Yin Jiuli; Tian Lixin; Fan Xinghua

    2010-01-01

    In this paper, we prove that the modified Camassa-Holm equation is Painleve integrable. We also study the orbital stability problem of negative solitary waves for this integrable equation. It is shown that the negative solitary waves are stable for arbitrary wave speed of propagation.

  18. Stability of plane wave solutions of the two-space-dimensional nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Martin, D.U.; Yuen, H.C.; Saffman, P.G.

    1980-01-01

    The stability of plane, periodic solutions of the two-dimensional nonlinear Schroedinger equation to infinitesimal, two-dimensional perturbation has been calculated and verified numerically. For standing wave disturbances, instability is found for both odd and even modes; as the period of the unperturbed solution increases, the instability associated with the odd modes remains but that associated with the even mode disappears, which is consistent with the results of Zakharov and Rubenchik, Saffman and Yuen and Ablowitz and Segur on the stability of solitons. In addition, we have identified travelling wave instabilities for the even mode perturbations which are absent in the long-wave limit. Extrapolation to the case of an unperturbed solution with infinite period suggests that these instabilities may also be present for the soliton. In other words, the soliton is unstable to odd, standing-wave perturbations, and very likely also to even, travelling-wave perturbations. (orig.)

  19. A One-Dimensional Wave Equation with White Noise Boundary Condition

    International Nuclear Information System (INIS)

    Kim, Jong Uhn

    2006-01-01

    We discuss the Cauchy problem for a one-dimensional wave equation with white noise boundary condition. We also establish the existence of an invariant measure when the noise is additive. Similar problems for parabolic equations were discussed by several authors. To our knowledge, there is only one work which investigated the initial-boundary value problem for a wave equation with random noise at the boundary. We handle a more general case by a different method. Our result on the existence of an invariant measure relies on the author's recent work on a certain class of stochastic evolution equations

  20. Symmetries and conserved quantities of discrete wave equation associated with the Ablowitz—Ladik—Lattice system

    International Nuclear Information System (INIS)

    Fu Jing-Li; He Yu-Fang; Hong Fang-Yu; Song Duan; Fu Hao

    2013-01-01

    In this paper, we present a new method to obtain the Lie symmetries and conserved quantities of the discrete wave equation with the Ablowitz—Ladik—Lattice equations. Firstly, the wave equation is transformed into a simple difference equation with the Ablowitz—Ladik—Lattice method. Secondly, according to the invariance of the discrete wave equation and the Ablowitz—Ladik—Lattice equations under infinitesimal transformation of dependent and independent variables, we derive the discrete determining equation and the discrete restricted equations. Thirdly, a series of the discrete analogs of conserved quantities, the discrete analogs of Lie groups, and the characteristic equations are obtained for the wave equation. Finally, we study a model of a biological macromolecule chain of mechanical behaviors, the Lie symmetry theory of discrete wave equation with the Ablowitz—Ladik—Lattice method is verified. (general)

  1. Partial Differential Equations and Solitary Waves Theory

    CERN Document Server

    Wazwaz, Abdul-Majid

    2009-01-01

    "Partial Differential Equations and Solitary Waves Theory" is a self-contained book divided into two parts: Part I is a coherent survey bringing together newly developed methods for solving PDEs. While some traditional techniques are presented, this part does not require thorough understanding of abstract theories or compact concepts. Well-selected worked examples and exercises shall guide the reader through the text. Part II provides an extensive exposition of the solitary waves theory. This part handles nonlinear evolution equations by methods such as Hirota’s bilinear method or the tanh-coth method. A self-contained treatment is presented to discuss complete integrability of a wide class of nonlinear equations. This part presents in an accessible manner a systematic presentation of solitons, multi-soliton solutions, kinks, peakons, cuspons, and compactons. While the whole book can be used as a text for advanced undergraduate and graduate students in applied mathematics, physics and engineering, Part II w...

  2. Experimental and numerical study of the wave run-up along a vertical plate

    DEFF Research Database (Denmark)

    Molin, Bernard; Kimmoun, O.; Liu, Y.

    2010-01-01

    Results from experiments on wave interaction with a rigid vertical plate are reported. The 5m long plate is set against the wall of a 30m wide basin, at 100m from the wavemaker. This set-up is equivalent to a 10m plate in the middle of a 60m wide basin. Regular waves are produced, with wavelength...... on extended Boussinesq equations. In most of the experimental tests, despite the large distance from the wavemaker to the plate and the small amplitude of the incident wave, no steady state is attained by the end of the exploitable part of the records....

  3. Capillary waves at the interface of two Bose–Einstein condensates. Long wavelengths asymptotic by trial function approach

    International Nuclear Information System (INIS)

    Mishonov, T.M.

    2015-01-01

    The dispersion relation for capillary waves at the boundary of two different Bose condensates is investigated using a trial wave-function approach applied to the Gross-Pitaevskii (GP) equations. The surface tension is expressed by the parameters of the GP equations. In the long wave-length limit the usual dispersion relation is re-derived while for wavelengths comparable to the healing length we predict significant deviations from the ω ∝ k 3/2 law which can be experimentally observed. We approximate the wave variables by a frozen order parameter, i.e. the wave function is frozen in the superfluid analogous to the magnetic field in highly conductive space plasmas. PACS codes: 67.85.Jk

  4. Asymptotic properties of spherically symmetric, regular and static solutions to Yang-Mills equations

    International Nuclear Information System (INIS)

    Cronstrom, C.

    1987-01-01

    In this paper the author discusses the asymptotic properties of solutions to Yang-Mills equations with the gauge group SU(2), for spherically symmetric, regular and static potentials. It is known, that the pure Yang-Mills equations cannot have nontrivial regular solutions which vanish rapidly at space infinity (socalled finite energy solutions). So, if regular solutions exist, they must have non-trivial asymptotic properties. However, if the asymptotic behaviour of the solutions is non-trivial, then the fact must be explicitly taken into account in constructing the proper action (and energy) for the theory. The elucidation of the appropriate surface correction to the Yang-Mills action (and hence the energy-momentum tensor density) is one of the main motivations behind the present study. In this paper the author restricts to the asymptotic behaviour of the static solutions. It is shown that this asymptotic behaviour is such that surface corrections (at space-infinity) are needed in order to obtain a well-defined (classical) theory. This is of relevance in formulating a quantum Yang-Mills theory

  5. Wave-equation Migration Velocity Analysis Using Plane-wave Common Image Gathers

    KAUST Repository

    Guo, Bowen; Schuster, Gerard T.

    2017-01-01

    Wave-equation migration velocity analysis (WEMVA) based on subsurface-offset, angle domain or time-lag common image gathers (CIGs) requires significant computational and memory resources because it computes higher dimensional migration images

  6. Skeletonized Least Squares Wave Equation Migration

    KAUST Repository

    Zhan, Ge; Schuster, Gerard T.

    2010-01-01

    of the wave equation. Only the early‐arrivals of these Green's functions are saved and skeletonized to form the migration Green's function (MGF) by convolution. Then the migration image is obtained by a dot product between the recorded shot gathers and the MGF

  7. Position difference regularity of corresponding R-wave peaks for maternal ECG components from different abdominal points

    International Nuclear Information System (INIS)

    Zhang Jie-Min; Liu Hong-Xing; Huang Xiao-Lin; Si Jun-Feng; Guan Qun; Tang Li-Ming; Liu Tie-Bing

    2014-01-01

    We collected 343 groups of abdominal electrocardiogram (ECG) data from 78 pregnant women and deleted the channels unable for experts to determine R-wave peaks from them; then, based on these filtered data, the statistics of position difference of corresponding R-wave peaks for different maternal ECG components from different points were studied. The resultant statistics showed the regularity that the position difference of corresponding maternal R-wave peaks between different abdominal points does not exceed the range of 30 ms. The regularity was also proved using the fECG data from MIT—BIH PhysioBank. Additionally, the paper applied the obtained regularity, the range of position differences of the corresponding maternal R-wave peaks, to accomplish the automatic detection of maternal R-wave peaks in the recorded all initial 343 groups of abdominal signals, including the ones with the largest fetal ECG components, and all 55 groups of ECG data from MIT—BIH PhysioBank, achieving the successful separation of the maternal ECGs. (interdisciplinary physics and related areas of science and technology)

  8. Wave-equation Migration Velocity Analysis Using Plane-wave Common Image Gathers

    KAUST Repository

    Guo, Bowen

    2017-06-01

    Wave-equation migration velocity analysis (WEMVA) based on subsurface-offset, angle domain or time-lag common image gathers (CIGs) requires significant computational and memory resources because it computes higher dimensional migration images in the extended image domain. To mitigate this problem, a WEMVA method using plane-wave CIGs is presented. Plane-wave CIGs reduce the computational cost and memory storage because they are directly calculated from prestack plane-wave migration, and the number of plane waves is often much smaller than the number of shots. In the case of an inaccurate migration velocity, the moveout of plane-wave CIGs is automatically picked by a semblance analysis method, which is then linked to the migration velocity update by a connective function. Numerical tests on two synthetic datasets and a field dataset validate the efficiency and effectiveness of this method.

  9. Integral Equation Methods for Electromagnetic and Elastic Waves

    CERN Document Server

    Chew, Weng; Hu, Bin

    2008-01-01

    Integral Equation Methods for Electromagnetic and Elastic Waves is an outgrowth of several years of work. There have been no recent books on integral equation methods. There are books written on integral equations, but either they have been around for a while, or they were written by mathematicians. Much of the knowledge in integral equation methods still resides in journal papers. With this book, important relevant knowledge for integral equations are consolidated in one place and researchers need only read the pertinent chapters in this book to gain important knowledge needed for integral eq

  10. Relativistic wave equations without the Velo-Zwanziger pathology

    International Nuclear Information System (INIS)

    Khalil, M.A.K.

    1976-06-01

    For particles described by relativistic wave equations of the form: (-iGAMMA x delta + m) psi(x) = 0 interacting with an external field B(x) it is known that the ''noncausal'' propagation characteristics are not present when (1) GAMMA 0 is diagonalizable and (2) B(x) = -eGAMMA/sub mu/A/sup mu/(x) (Amar--Dozzio). The ''noncausality''difficulties arise for the Rarita--Schwinger spin 3 / 2 equation, with nondiagonalizable GAMMA 0 , in minimal coupling (i.e., B(x) = -eGAMMA x A(x)) and the PDK spin 1 equation, with diagonalizable GAMMA 0 , in a quadrupole coupling (Velo--Zwanziger) where either (1) or (2) of the Amar--Dozzio (sufficient) conditions are violated. Some sufficient conditions are derived and explored where the Velo--Zwanziger ''noncausality'' pathology can be avoided, even though one, or the other, or both of the conditions (1) and (2) are violated. Examples with both reducible and irreducible wave equations are included

  11. Global existence and nonexistence for the viscoelastic wave equation with nonlinear boundary damping-source interaction

    KAUST Repository

    Said-Houari, Belkacem

    2012-09-01

    The goal of this work is to study a model of the viscoelastic wave equation with nonlinear boundary/interior sources and a nonlinear interior damping. First, applying the Faedo-Galerkin approximations combined with the compactness method to obtain existence of regular global solutions to an auxiliary problem with globally Lipschitz source terms and with initial data in the potential well. It is important to emphasize that it is not possible to consider density arguments to pass from regular to weak solutions if one considers regular solutions of our problem where the source terms are locally Lipschitz functions. To overcome this difficulty, we use an approximation method involving truncated sources and adapting the ideas in [13] to show that the existence of weak solutions can still be obtained for our problem. Second, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term, then the solution ceases to exist and blows up in finite time provided that the initial data are large enough.

  12. Global existence and nonexistence for the viscoelastic wave equation with nonlinear boundary damping-source interaction

    KAUST Repository

    Said-Houari, Belkacem; Nascimento, Flá vio A Falcã o

    2012-01-01

    The goal of this work is to study a model of the viscoelastic wave equation with nonlinear boundary/interior sources and a nonlinear interior damping. First, applying the Faedo-Galerkin approximations combined with the compactness method to obtain existence of regular global solutions to an auxiliary problem with globally Lipschitz source terms and with initial data in the potential well. It is important to emphasize that it is not possible to consider density arguments to pass from regular to weak solutions if one considers regular solutions of our problem where the source terms are locally Lipschitz functions. To overcome this difficulty, we use an approximation method involving truncated sources and adapting the ideas in [13] to show that the existence of weak solutions can still be obtained for our problem. Second, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term, then the solution ceases to exist and blows up in finite time provided that the initial data are large enough.

  13. Ginzburg-Landau equation as a heuristic model for generating rogue waves

    Science.gov (United States)

    Lechuga, Antonio

    2016-04-01

    Envelope equations have many applications in the study of physical systems. Particularly interesting is the case 0f surface water waves. In steady conditions, laboratory experiments are carried out for multiple purposes either for researches or for practical problems. In both cases envelope equations are useful for understanding qualitative and quantitative results. The Ginzburg-Landau equation provides an excellent model for systems of that kind with remarkable patterns. Taking into account the above paragraph the main aim of our work is to generate waves in a water tank with almost a symmetric spectrum according to Akhmediev (2011) and thus, to produce a succession of rogue waves. The envelope of these waves gives us some patterns whose model is a type of Ginzburg-Landau equation, Danilov et al (1988). From a heuristic point of view the link between the experiment and the model is achieved. Further, the next step consists of changing generating parameters on the water tank and also the coefficients of the Ginzburg-Landau equation, Lechuga (2013) in order to reach a sufficient good approach.

  14. Approximate equations at breaking for nearshore wave transformation coefficients

    Digital Repository Service at National Institute of Oceanography (India)

    Chandramohan, P.; Nayak, B.U.; SanilKumar, V.

    Based on small amplitude wave theory approximate equations are evaluated for determining the coefficients of shoaling, refraction, bottom friction, bottom percolation and viscous dissipation at breaking. The results obtainEd. by these equations...

  15. A multiresolution method for solving the Poisson equation using high order regularization

    DEFF Research Database (Denmark)

    Hejlesen, Mads Mølholm; Walther, Jens Honore

    2016-01-01

    We present a novel high order multiresolution Poisson solver based on regularized Green's function solutions to obtain exact free-space boundary conditions while using fast Fourier transforms for computational efficiency. Multiresolution is a achieved through local refinement patches and regulari......We present a novel high order multiresolution Poisson solver based on regularized Green's function solutions to obtain exact free-space boundary conditions while using fast Fourier transforms for computational efficiency. Multiresolution is a achieved through local refinement patches...... and regularized Green's functions corresponding to the difference in the spatial resolution between the patches. The full solution is obtained utilizing the linearity of the Poisson equation enabling super-position of solutions. We show that the multiresolution Poisson solver produces convergence rates...

  16. Asymptotic solutions and spectral theory of linear wave equations

    International Nuclear Information System (INIS)

    Adam, J.A.

    1982-01-01

    This review contains two closely related strands. Firstly the asymptotic solution of systems of linear partial differential equations is discussed, with particular reference to Lighthill's method for obtaining the asymptotic functional form of the solution of a scalar wave equation with constant coefficients. Many of the applications of this technique are highlighted. Secondly, the methods and applications of the theory of the reduced (one-dimensional) wave equation - particularly spectral theory - are discussed. While the breadth of application and power of the techniques is emphasised throughout, the opportunity is taken to present to a wider readership, developments of the methods which have occured in some aspects of astrophysical (particularly solar) and geophysical fluid dynamics. It is believed that the topics contained herein may be of relevance to the applied mathematician or theoretical physicist interest in problems of linear wave propagation in these areas. (orig./HSI)

  17. Low regularity solutions of the Chern-Simons-Higgs equations in the Lorentz gauge

    Directory of Open Access Journals (Sweden)

    Nikolaos Bournaveas

    2009-09-01

    Full Text Available We prove local well-posedness for the 2+1-dimensional Chern-Simons-Higgs equations in the Lorentz gauge with initial data of low regularity. Our result improves earlier results by Huh [10, 11].

  18. Regularity criteria for the Navier–Stokes equations based on one component of velocity

    Czech Academy of Sciences Publication Activity Database

    Guo, Z.; Caggio, M.; Skalák, Zdeněk

    2017-01-01

    Roč. 35, June (2017), s. 379-396 ISSN 1468-1218 R&D Projects: GA ČR GA14-02067S Grant - others:Západočeská univerzita(CZ) SGS-2016-003; National Natural Science Foundation of China (CN) 11301394 Institutional support: RVO:67985874 Keywords : Navier–Stokes equations * regularity of solutions * regularity criteria * Anisotropic Lebesgue spaces Subject RIV: BK - Fluid Dynamics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 1.659, year: 2016

  19. Regularity criteria for the Navier–Stokes equations based on one component of velocity

    Czech Academy of Sciences Publication Activity Database

    Guo, Z.; Caggio, M.; Skalák, Zdeněk

    2017-01-01

    Roč. 35, June (2017), s. 379-396 ISSN 1468-1218 R&D Projects: GA ČR GA14-02067S Grant - others:Západočeská univerzita(CZ) SGS-2016-003; National Natural Science Foundation of China(CN) 11301394 Institutional support: RVO:67985874 Keywords : Navier–Stokes equations * regularity of solutions * regularity criteria * Anisotropic Lebesgue spaces Subject RIV: BK - Fluid Dynamics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 1.659, year: 2016

  20. Waves in plasmas (part 1 - wave-plasma interaction general background)

    International Nuclear Information System (INIS)

    Dumont, R.

    2004-01-01

    This document gathers a series of transparencies presented in the framework of the week-long lectures 'hot plasmas 2004' and dedicated to the physics of wave-plasma interaction. The structure of this document is as follows: 1) wave and diverse plasmas, 2) basic equations (Maxwell equations), 3) waves in a fluid plasma, and 4) waves in a kinetic plasma (collisionless plasma)

  1. Radio wave propagation and parabolic equation modeling

    CERN Document Server

    Apaydin, Gokhan

    2018-01-01

    A thorough understanding of electromagnetic wave propagation is fundamental to the development of sophisticated communication and detection technologies. The powerful numerical methods described in this book represent a major step forward in our ability to accurately model electromagnetic wave propagation in order to establish and maintain reliable communication links, to detect targets in radar systems, and to maintain robust mobile phone and broadcasting networks. The first new book on guided wave propagation modeling and simulation to appear in nearly two decades, Radio Wave Propagation and Parabolic Equation Modeling addresses the fundamentals of electromagnetic wave propagation generally, with a specific focus on radio wave propagation through various media. The authors explore an array of new applications, and detail various v rtual electromagnetic tools for solving several frequent electromagnetic propagation problems. All of the methods described are presented within the context of real-world scenari...

  2. Smooth, cusped, and discontinuous traveling waves in the periodic fluid resonance equation

    Science.gov (United States)

    Kruse, Matthew Thomas

    The principal motivation for this dissertation is to extend the study of small amplitude high frequency wave propagation in solutions for hyperbolic conservation laws begun by A. Majda and R. Rosales in 1984. It was then that Majda and Rosales obtained equations governing the leading order wave amplitudes of resonantly interacting weakly nonlinear high frequency wave trains in the compressible Euler equations. The equations were obtained through systematic application of multiple scales and result in a pair of nonlinear acoustic wave equations coupled through a convolution operator. The extended solutions satisfy a pair of inviscid Burgers' equations coupled via a spatial convolution operator. Since then, many mathematicians have used this technique to extend the time validity of solutions to systems of equations other than the Euler equations and have arrived at similar nonlinear non-local systems. This work attempts to look at some of the basic features of the linear and nonlinear coupled and decoupled non- local equations, offering some analytic solutions and numerical insight into the phenomena associated with these equations. We do so by examining a single non-local linear equation, and then a single equation coupling a Burgers' nonlinearity with a linear convolution operator. The linear case is completely solvable. Analytic solutions are provided along with numerical results showing the fundamental properties of the linear non- local equations. In the nonlinear case some analytic solutions, including steady state profiles and traveling wave solutions, are provided along with a battery of numerical simulations. Evidence indicates the existence of attractors for solutions of the single equation with a single mode kernel. Provided resonant interaction takes place, the profile of the attractor is uniquely dependent on the kernel alone. Hamiltonian equations are obtained for both the linear and nonlinear equations with the condition that the resonant kernel must

  3. Visco-acoustic wave-equation traveltime inversion and its sensitivity to attenuation errors

    KAUST Repository

    Yu, Han; Chen, Yuqing; Hanafy, Sherif M.; Huang, Jiangping

    2018-01-01

    A visco-acoustic wave-equation traveltime inversion method is presented that inverts for the shallow subsurface velocity distribution. Similar to the classical wave equation traveltime inversion, this method finds the velocity model that minimizes

  4. On an Acoustic Wave Equation Arising in Non-Equilibrium Gasdynamics. Classroom Notes

    Science.gov (United States)

    Chandran, Pallath

    2004-01-01

    The sixth-order wave equation governing the propagation of one-dimensional acoustic waves in a viscous, heat conducting gaseous medium subject to relaxation effects has been considered. It has been reduced to a system of lower order equations corresponding to the finite speeds occurring in the equation, following a method due to Whitham. The lower…

  5. The Appell transformation for the paraxial wave equation

    International Nuclear Information System (INIS)

    Torre, A

    2011-01-01

    Some issues related to the 1D heat equation are revisited and framed within the context of the free-space paraxial propagation, formally accounted for by the 2D paraxial wave equation. In particular, the Appell transformation, which is well known in the theory of the heat equation, is reformulated in optical terms, and accordingly interpreted in the light of the propagation of given source functions, which are in a definite relation with the source functions of the original wavefunctions. Basic to the discussion is the Lie-algebra-based approach, as developed in a series of seminal papers by Kalnins, Miller and Boyer, to evolutionary-type equations, ruled by Hamiltonian operators underlying a harmonic oscillator-like symmetry algebra. Indeed, both the heat equation and the paraxial wave equation are particular cases of this kind of equation. When interpreting such an approach in terms of the propagation of assigned 'source' functions, the transformations between wavefunctions may be traced back to definite relations between the respective source functions. Thus, the optical Appell transformation is seen to be a manifestation of the correspondence between wavefunctions generated by eigenstates of operators, which are linked through a Fourier-similarity transformation. As a mere consequence, one can introduce the fractional Appell transformation, thus displaying a family of symmetry transformations parameterized by a continuous parameter

  6. THE FUNDAMENTAL SOLUTIONS FOR MULTI-TERM MODIFIED POWER LAW WAVE EQUATIONS IN A FINITE DOMAIN.

    Science.gov (United States)

    Jiang, H; Liu, F; Meerschaert, M M; McGough, R J

    2013-01-01

    Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n ) ( n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko's Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi-term time-space fractional models including fractional Laplacian.

  7. Line Rogue Waves in the Mel'nikov Equation

    Science.gov (United States)

    Shi, Yongkang

    2017-07-01

    General line rogue waves in the Mel'nikov equation are derived via the Hirota bilinear method, which are given in terms of determinants whose matrix elements have plain algebraic expressions. It is shown that fundamental rogue waves are line rogue waves, which arise from the constant background with a line profile and then disappear into the constant background again. By means of the regulation of free parameters, two subclass of nonfundamental rogue waves are generated, which are called as multirogue waves and higher-order rogue waves. The multirogue waves consist of several fundamental line rogue waves, which arise from the constant background and then decay back to the constant background. The higher-order rogue waves start from a localised lump and retreat back to it. The dynamical behaviours of these line rogue waves are demonstrated by the density and the three-dimensional figures.

  8. THE FUNDAMENTAL SOLUTIONS FOR MULTI-TERM MODIFIED POWER LAW WAVE EQUATIONS IN A FINITE DOMAIN

    OpenAIRE

    Jiang, H.; Liu, F.; Meerschaert, M. M.; McGough, R. J.

    2013-01-01

    Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development.

  9. New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod

    Science.gov (United States)

    Seadawy, Aly R.; Manafian, Jalil

    2018-03-01

    This paper examines the effectiveness of an integration scheme which called the extended trial equation method (ETEM) in exactly solving a well-known nonlinear equation of partial differential equations (PDEs). In this respect, the longitudinal wave equation (LWE) that arises in mathematical physics with dispersion caused by the transverse Poisson's effect in a magneto-electro-elastic (MEE) circular rod, which a series of exact traveling wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of the longitudinal wave equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena of this longitudinal wave equation. Many other such types of nonlinear equations arising in non-destructive evaluation of structures made of the advanced MEE material can also be solved by this method.

  10. Boundary Equations and Regularity Theory for Geometric Variational Systems with Neumann Data

    Science.gov (United States)

    Schikorra, Armin

    2018-02-01

    We study boundary regularity of maps from two-dimensional domains into manifolds which are critical with respect to a generic conformally invariant variational functional and which, at the boundary, intersect perpendicularly with a support manifold. For example, harmonic maps, or H-surfaces, with a partially free boundary condition. In the interior it is known, by the celebrated work of Rivière, that these maps satisfy a system with an antisymmetric potential, from which one can derive the interior regularity of the solution. Avoiding a reflection argument, we show that these maps satisfy along the boundary a system of equations which also exhibits a (nonlocal) antisymmetric potential that combines information from the interior potential and the geometric Neumann boundary condition. We then proceed to show boundary regularity for solutions to such systems.

  11. Exact solitary waves of the Korteveg - de Vries - Burgers equation

    OpenAIRE

    Kudryashov, N. A.

    2004-01-01

    New approach is presented to search exact solutions of nonlinear differential equations. This method is used to look for exact solutions of the Korteveg -- de Vries -- Burgers equation. New exact solitary waves of the Korteveg -- de Vries -- Burgers equation are found.

  12. Existence and asymptotic behavior of the wave equation with dynamic boundary conditions

    KAUST Repository

    Graber, Philip Jameson; Said-Houari, Belkacem

    2012-01-01

    The goal of this work is to study a model of the strongly damped wave equation with dynamic boundary conditions and nonlinear boundary/interior sources and nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. In addition, we show that in the strongly damped case solutions gain additional regularity for positive times t>0. Second, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution grows as an exponential function. Moreover, in the absence of the strong damping term, we prove that the solution ceases to exists and blows up in finite time. © 2012 Springer Science+Business Media, LLC.

  13. Existence and asymptotic behavior of the wave equation with dynamic boundary conditions

    KAUST Repository

    Graber, Philip Jameson

    2012-03-07

    The goal of this work is to study a model of the strongly damped wave equation with dynamic boundary conditions and nonlinear boundary/interior sources and nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. In addition, we show that in the strongly damped case solutions gain additional regularity for positive times t>0. Second, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution grows as an exponential function. Moreover, in the absence of the strong damping term, we prove that the solution ceases to exists and blows up in finite time. © 2012 Springer Science+Business Media, LLC.

  14. Periodic solutions for one dimensional wave equation with bounded nonlinearity

    Science.gov (United States)

    Ji, Shuguan

    2018-05-01

    This paper is concerned with the periodic solutions for the one dimensional nonlinear wave equation with either constant or variable coefficients. The constant coefficient model corresponds to the classical wave equation, while the variable coefficient model arises from the forced vibrations of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. For finding the periodic solutions of variable coefficient wave equation, it is usually required that the coefficient u (x) satisfies ess infηu (x) > 0 with ηu (x) = 1/2 u″/u - 1/4 (u‧/u)2, which actually excludes the classical constant coefficient model. For the case ηu (x) = 0, it is indicated to remain an open problem by Barbu and Pavel (1997) [6]. In this work, for the periods having the form T = 2p-1/q (p , q are positive integers) and some types of boundary value conditions, we find some fundamental properties for the wave operator with either constant or variable coefficients. Based on these properties, we obtain the existence of periodic solutions when the nonlinearity is monotone and bounded. Such nonlinearity may cross multiple eigenvalues of the corresponding wave operator. In particular, we do not require the condition ess infηu (x) > 0.

  15. Relativistic n-body wave equations in scalar quantum field theory

    International Nuclear Information System (INIS)

    Emami-Razavi, Mohsen

    2006-01-01

    The variational method in a reformulated Hamiltonian formalism of Quantum Field Theory (QFT) is used to derive relativistic n-body wave equations for scalar particles (bosons) interacting via a massive or massless mediating scalar field (the scalar Yukawa model). Simple Fock-space variational trial states are used to derive relativistic n-body wave equations. The equations are shown to have the Schroedinger non-relativistic limits, with Coulombic interparticle potentials in the case of a massless mediating field and Yukawa interparticle potentials in the case of a massive mediating field. Some examples of approximate ground state solutions of the n-body relativistic equations are obtained for various strengths of coupling, for both massive and massless mediating fields

  16. Drift of Spiral Waves in Complex Ginzburg-Landau Equation

    International Nuclear Information System (INIS)

    Yang Junzhong; Zhang Mei

    2006-01-01

    The spontaneous drift of the spiral wave in a finite domain in the complex Ginzburg-Landau equation is investigated numerically. By using the interactions between the spiral wave and its images, we propose a phenomenological theory to explain the observations.

  17. A regularity criterion for the Navier-Stokes equations based on the gradient of one velocity component

    Czech Academy of Sciences Publication Activity Database

    Skalák, Zdeněk

    2016-01-01

    Roč. 437, č. 1 (2016), s. 474-484 ISSN 0022-247X R&D Projects: GA ČR GA14-02067S Institutional support: RVO:67985874 Keywords : Navier - Stokes equations * regularity of solutions * regularity criteria Subject RIV: BK - Fluid Dynamics Impact factor: 1.064, year: 2016

  18. Anisotropic wave-equation traveltime and waveform inversion

    KAUST Repository

    Feng, Shihang; Schuster, Gerard T.

    2016-01-01

    The wave-equation traveltime and waveform inversion (WTW) methodology is developed to invert for anisotropic parameters in a vertical transverse isotropic (VTI) meidum. The simultaneous inversion of anisotropic parameters v0, ε and δ is initially

  19. Inaccuracy caused by the use of thermodynamic equation inside shock wave front

    International Nuclear Information System (INIS)

    Sano, Yukio; Abe, Akihisa; Tokushima, Koji; Arathoon, P.

    1998-01-01

    The aim of this study is to examine the difference between shock temperatures predicted by an equation for temperature inside a steady wave front and the Walsh-Christian equation. Calculations are for yttria-doped tetragonal zirconia, which shows an elastic-plastic and a phase transition: Thus the shock waves treated are multiple structure waves composed of one to three steady wave fronts. The evaluated temperature was 3350K at the minimum specific volume of 0.1175 cm 3 /g (or maximum Hugoniot shock pressure of 140GPa) considered in the present examination, while the temperature predicted by the Walsh-Christian equation under identical conditions was 2657K. The cause of the large temperature discrepancy is considered to be that the present model treats nonequilibrium states inside steady waves

  20. On the solution of the equations for nonlinear interaction of three damped waves

    International Nuclear Information System (INIS)

    1976-01-01

    Three-wave interactions are analyzed in a coherent wave description assuming different linear damping (or growth) of the individual waves. It is demonstrated that when two of the coefficients of dissipation are equal, the set of equations can be reduced to a single equivalent equation, which in the nonlinearly unstable case, where one wave is undamped, asymptotically takes the form of an equation defining the third Painleve transcendent. It is then possible to find an asymptotic expansion near the time of explosion. This solution is of principal interest since it indicates that the solution of the general three-wave system, where the waves undergo different individual dissipations, belongs to a higher class of functions, which reduces to Jacobian elliptic functions only in the case where all waves suffer the same damping [fr

  1. Long-term wave measurements in a climate change perspective.

    Science.gov (United States)

    Pomaro, Angela; Bertotti, Luciana; Cavaleri, Luigi; Lionello, Piero; Portilla-Yandun, Jesus

    2017-04-01

    At present multi-decadal time series of wave data needed for climate studies are generally provided by long term model simulations (hindcasts) covering the area of interest. Examples, among many, at different scales are wave hindcasts adopting the wind fields of the ERA-Interim reanalysis of the European Centre for Medium-Range Weather Forecasts (ECMWF, Reading, U.K.) at the global level and by regional re-analysis as for the Mediterranean Sea (Lionello and Sanna, 2006). Valuable as they are, these estimates are necessarily affected by the approximations involved, the more so because of the problems encountered within modelling processes in small basins using coarse resolution wind fields (Cavaleri and Bertotti, 2004). On the contrary, multi-decadal observed time series are rare. They have the evident advantage of somehow representing the real evolution of the waves, without the shortcomings associated with the limitation of models in reproducing the actual processes and the real variability within the wave fields. Obviously, observed wave time series are not exempt of problems. They represent a very local information, hence their use to describe the wave evolution at large scale is sometimes arguable and, in general, it needs the support of model simulations assessing to which extent the local value is representative of a large scale evolution. Local effects may prevent the identification of trends that are indeed present at large scale. Moreover, a regular maintenance, accurate monitoring and metadata information are crucial issues when considering the reliability of a time series for climate applications. Of course, where available, especially if for several decades, measured data are of great value for a number of reasons and can be valuable clues to delve further into the physics of the processes of interest, especially if considering that waves, as an integrated product of the local climate, if available in an area sensitive to even limited changes of the

  2. Propagation of Tsunami-like Surface Long Waves in the Bays of a Variable Depth

    Directory of Open Access Journals (Sweden)

    A.Yu. Bazykina

    2016-08-01

    Full Text Available Within the framework of the nonlinear long wave theory the regularities of solitary long wave propagation in the semi-closed bays of model and real geometry are numerically studied. In the present article the zones of wave amplification in the bay are found. The first one is located near the wave running-up on the beach (in front of the bay entrance and the other one – in the middle part of the sea basin. Wave propagation in these zones is accompanied both by significant rise and considerable fall of the sea level. Narrowing of the bay entrance and increase of the entering wave length result in decrease of the sea level maximum rises and falls. The Feodosiya Gulf in the Black Sea is considered as a real basin. In general the dynamics of the waves in the gulf is similar to wave dynamics in the model bay. Four zones of the strongest wave amplification in the Feodosiya Gulf are revealed in the article. The sea level maximum rises and extreme falls which tend to grow with decrease of the entering wave length are observed in these zones. The distance traveled by the wave before the collapse (due to non-linear effects, was found to reduce with decreasing wavelength of the entrance to the bay (gulf.

  3. Symmetries of the triple degenerate DNLS equations for weakly nonlinear dispersive MHD waves

    International Nuclear Information System (INIS)

    Webb, G. M.; Brio, M.; Zank, G. P.

    1996-01-01

    A formulation of Hamiltonian and Lagrangian variational principles, Lie point symmetries and conservation laws for the triple degenerate DNLS equations describing the propagation of weakly nonlinear dispersive MHD waves along the ambient magnetic field, in β∼1 plasmas is given. The equations describe the interaction of the Alfven and magnetoacoustic modes near the triple umbilic point, where the fast magnetosonic, slow magnetosonic and Alfven speeds coincide and a g 2 =V A 2 where a g is the gas sound speed and V A is the Alfven speed. A discussion is given of the travelling wave similarity solutions of the equations, which include solitary wave and periodic traveling waves. Strongly compressible solutions indicate the necessity for the insertion of shocks in the flow, whereas weakly compressible, near Alfvenic solutions resemble similar, shock free travelling wave solutions of the DNLS equation

  4. Invariant measures for stochastic nonlinear beam and wave equations

    Czech Academy of Sciences Publication Activity Database

    Brzezniak, Z.; Ondreját, Martin; Seidler, Jan

    2016-01-01

    Roč. 260, č. 5 (2016), s. 4157-4179 ISSN 0022-0396 R&D Projects: GA ČR GAP201/10/0752 Institutional support: RVO:67985556 Keywords : stochastic partial differential equation * stochastic beam equation * stochastic wave equation * invariant measure Subject RIV: BA - General Mathematics Impact factor: 1.988, year: 2016 http://library.utia.cas.cz/separaty/2016/SI/ondrejat-0453412.pdf

  5. Application of Littlewood-Paley decomposition to the regularity of Boltzmann type kinetic equations; Application de la decomposition de Littlewood-Paley a la regularite pour des equations cinetiques de type Boltzmann

    Energy Technology Data Exchange (ETDEWEB)

    EL Safadi, M

    2007-03-15

    We study the regularity of kinetic equations of Boltzmann type.We use essentially Littlewood-Paley method from harmonic analysis, consisting mainly in working with dyadics annulus. We shall mainly concern with the homogeneous case, where the solution f(t,x,v) depends only on the time t and on the velocities v, while working with realistic and singular cross-sections (non cutoff). In the first part, we study the particular case of Maxwellian molecules. Under this hypothesis, the structure of the Boltzmann operator and his Fourier transform write in a simple form. We show a global C{sup {infinity}} regularity. Then, we deal with the case of general cross-sections with 'hard potential'. We are interested in the Landau equation which is limit equation to the Boltzmann equation, taking in account grazing collisions. We prove that any weak solution belongs to Schwartz space S. We demonstrate also a similar regularity for the case of Boltzmann equation. Let us note that our method applies directly for all dimensions, and proofs are often simpler compared to other previous ones. Finally, we finish with Boltzmann-Dirac equation. In particular, we adapt the result of regularity obtained in Alexandre, Desvillettes, Wennberg and Villani work, using the dissipation rate connected with Boltzmann-Dirac equation. (author)

  6. Travelling Solitary Wave Solutions for Generalized Time-delayed Burgers-Fisher Equation

    International Nuclear Information System (INIS)

    Deng Xijun; Han Libo; Li Xi

    2009-01-01

    In this paper, travelling wave solutions for the generalized time-delayed Burgers-Fisher equation are studied. By using the first-integral method, which is based on the ring theory of commutative algebra, we obtain a class of travelling solitary wave solutions for the generalized time-delayed Burgers-Fisher equation. A minor error in the previous article is clarified. (general)

  7. Separation of variables for the nonlinear wave equation in polar coordinates

    International Nuclear Information System (INIS)

    Shermenev, Alexander

    2004-01-01

    Some classical types of nonlinear wave motion in polar coordinates are studied within quadratic approximation. When the nonlinear quadratic terms in the wave equation are arbitrary, the usual perturbation techniques used in polar coordinates leads to overdetermined systems of linear algebraic equations for the unknown coefficients. However, we show that these overdetermined systems are compatible with the special case of the nonlinear shallow water equation and express explicitly the coefficients of the first two harmonics as polynomials of the Bessel functions of radius and of the trigonometric functions of angle. It gives a series of solutions to the nonlinear shallow water equation that are periodic in time and found with the same accuracy as the equation is derived

  8. Rarita-Schwinger field and multicomponent wave equation

    International Nuclear Information System (INIS)

    Kaloshin, A.E.; Lomov, V.P.

    2011-01-01

    We suggest a simple method to solve a wave equation for Rarita-Schwinger field without additional constraints. This method based on the use of off-shell projection operators allows one to diagonalize spin-1/2 sector of the field

  9. A rapid numerical method for solving Serre-Green-Naghdi equations describing long free surface gravity waves

    Science.gov (United States)

    Favrie, N.; Gavrilyuk, S.

    2017-07-01

    A new numerical method for solving the Serre-Green-Naghdi (SGN) equations describing dispersive waves on shallow water is proposed. From the mathematical point of view, the SGN equations are the Euler-Lagrange equations for a ‘master’ lagrangian submitted to a differential constraint which is the mass conservation law. One major numerical challenge in solving the SGN equations is the resolution of an elliptic problem at each time instant. This is the most time-consuming part of the numerical method. The idea is to replace the ‘master’ lagrangian by a one-parameter family of ‘augmented’ lagrangians, depending on a greater number of variables, for which the corresponding Euler-Lagrange equations are hyperbolic. In such an approach, the ‘master’ lagrangian is recovered by the augmented lagrangian in some limit (for example, when the corresponding parameter is large). The choice of such a family of augmented lagrangians is proposed and discussed. The corresponding hyperbolic system is numerically solved by a Godunov type method. Numerical solutions are compared with exact solutions to the SGN equations. It appears that the computational time in solving the hyperbolic system is much lower than in the case where the elliptic operator is inverted. The new method is applied, in particular, to the study of ‘Favre waves’ representing non-stationary undular bores produced after reflection of the fluid flow with a free surface at an immobile wall.

  10. Two types of nonlinear wave equations for diffractive beams in bubbly liquids with nonuniform bubble number density.

    Science.gov (United States)

    Kanagawa, Tetsuya

    2015-05-01

    This paper theoretically treats the weakly nonlinear propagation of diffracted sound beams in nonuniform bubbly liquids. The spatial distribution of the number density of the bubbles, initially in a quiescent state, is assumed to be a slowly varying function of the spatial coordinates; the amplitude of variation is assumed to be small compared to the mean number density. A previous derivation method of nonlinear wave equations for plane progressive waves in uniform bubbly liquids [Kanagawa, Yano, Watanabe, and Fujikawa (2010). J. Fluid Sci. Technol. 5(3), 351-369] is extended to handle quasi-plane beams in weakly nonuniform bubbly liquids. The diffraction effect is incorporated by adding a relation that scales the circular sound source diameter to the wavelength into the original set of scaling relations composed of nondimensional physical parameters. A set of basic equations for bubbly flows is composed of the averaged equations of mass and momentum, the Keller equation for bubble wall, and supplementary equations. As a result, two types of evolution equations, a nonlinear Schrödinger equation including dissipation, diffraction, and nonuniform effects for high-frequency short-wavelength case, and a Khokhlov-Zabolotskaya-Kuznetsov equation including dispersion and nonuniform effects for low-frequency long-wavelength case, are derived from the basic set.

  11. A Relation Between the Eikonal Equation Associated to a Potential Energy Surface and a Hyperbolic Wave Equation.

    Science.gov (United States)

    Bofill, Josep Maria; Quapp, Wolfgang; Caballero, Marc

    2012-12-11

    The potential energy surface (PES) of a molecule can be decomposed into equipotential hypersurfaces. We show in this article that the hypersurfaces are the wave fronts of a certain hyperbolic partial differential equation, a wave equation. It is connected with the gradient lines, or the steepest descent, or the steepest ascent lines of the PES. The energy seen as a reaction coordinate plays the central role in this treatment.

  12. Computational study on full-wave inversion based on the acoustic wave-equation; Onkyoha hado hoteishiki full wave inversion no model keisan ni yoru kento

    Energy Technology Data Exchange (ETDEWEB)

    Watanabe, T; Sassa, K [Kyoto University, Kyoto (Japan); Uesaka, S [Kyoto University, Kyoto (Japan). Faculty of Engineering

    1996-10-01

    The effect of initial models on full-wave inversion (FWI) analysis based on acoustic wave-equation was studied for elastic wave tomography of underground structures. At present, travel time inversion using initial motion travel time is generally used, and inverse analysis is conducted using the concept `ray,` assuming very high wave frequency. Although this method can derive stable solutions relatively unaffected by initial model, it uses only the data of initial motion travel time. FWI calculates theoretical waveform at each receiver using all of observed waveforms as data by wave equation modeling where 2-D underground structure is calculated by difference calculus under the assumption that wave propagation is described by wave equation of P wave. Although it is a weak point that FWI is easily affected by noises in an initial model and data, it is featured by high resolution of solutions. This method offers very excellent convergence as a proper initial model is used, resulting in sufficient performance, however, it is strongly affected by initial model. 2 refs., 7 figs., 1 tab.

  13. The periodic wave solutions for the (2 + 1)-dimensional Konopelchenko-Dubrovsky equations

    International Nuclear Information System (INIS)

    Sheng Zhang

    2006-01-01

    More periodic wave solutions expressed by Jacobi elliptic functions for the (2 + 1)-dimensional Konopelchenko-Dubrovsky equations are obtained by using the extended F-expansion method. In the limit cases, the solitary wave solutions and trigonometric function solutions for the equations are also obtained

  14. The non-local Fisher–KPP equation: travelling waves and steady states

    International Nuclear Information System (INIS)

    Berestycki, Henri; Nadin, Grégoire; Perthame, Benoit; Ryzhik, Lenya

    2009-01-01

    We consider the Fisher–KPP equation with a non-local saturation effect defined through an interaction kernel φ(x) and investigate the possible differences with the standard Fisher–KPP equation. Our first concern is the existence of steady states. We prove that if the Fourier transform φ-circumflex(ξ) is positive or if the length σ of the non-local interaction is short enough, then the only steady states are u ≡ 0 and u ≡ 1. Next, we study existence of the travelling waves. We prove that this equation admits travelling wave solutions that connect u = 0 to an unknown positive steady state u ∞ (x), for all speeds c ≥ c * . The travelling wave connects to the standard state u ∞ (x) ≡ 1 under the aforementioned conditions: φ-circumflex(ξ) > 0 or σ is sufficiently small. However, the wave is not monotonic for σ large

  15. Long-Term Dynamics of Autonomous Fractional Differential Equations

    Science.gov (United States)

    Liu, Tao; Xu, Wei; Xu, Yong; Han, Qun

    This paper aims to investigate long-term dynamic behaviors of autonomous fractional differential equations with effective numerical method. The long-term dynamic behaviors predict where systems are heading after long-term evolution. We make some modification and transplant cell mapping methods to autonomous fractional differential equations. The mapping time duration of cell mapping is enlarged to deal with the long memory effect. Three illustrative examples, i.e. fractional Lotka-Volterra equation, fractional van der Pol oscillator and fractional Duffing equation, are studied with our revised generalized cell mapping method. We obtain long-term dynamics, such as attractors, basins of attraction, and saddles. Compared with some existing stability and numerical results, the validity of our method is verified. Furthermore, we find that the fractional order has its effect on the long-term dynamics of autonomous fractional differential equations.

  16. Diffusion phenomenon for linear dissipative wave equations in an exterior domain

    Science.gov (United States)

    Ikehata, Ryo

    Under the general condition of the initial data, we will derive the crucial estimates which imply the diffusion phenomenon for the dissipative linear wave equations in an exterior domain. In order to derive the diffusion phenomenon for dissipative wave equations, the time integral method which was developed by Ikehata and Matsuyama (Sci. Math. Japon. 55 (2002) 33) plays an effective role.

  17. Classification of All Single Travelling Wave Solutions to Calogero-Degasperis-Focas Equation

    International Nuclear Information System (INIS)

    Liu Chengshi

    2007-01-01

    Under the travelling wave transformation, Calogero-Degasperis-Focas equation is reduced to an ordinary differential equation. Using a symmetry group of one parameter, this ODE is reduced to a second-order linear inhomogeneous ODE. Furthermore, we apply the change of the variable and complete discrimination system for polynomial to solve the corresponding integrals and obtained the classification of all single travelling wave solutions to Calogero-Degasperis-Focas equation.

  18. Partial differential equations

    CERN Document Server

    Evans, Lawrence C

    2010-01-01

    This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...

  19. Numerical study of traveling-wave solutions for the Camassa-Holm equation

    International Nuclear Information System (INIS)

    Kalisch, Henrik; Lenells, Jonatan

    2005-01-01

    We explore numerically different aspects of periodic traveling-wave solutions of the Camassa-Holm equation. In particular, the time evolution of some recently found new traveling-wave solutions and the interaction of peaked and cusped waves is studied

  20. Jacobian elliptic wave solutions for the Wadati-Segur-Ablowitz equation

    International Nuclear Information System (INIS)

    Teh, C.G.R.; Koo, W.K.; Lee, B.S.

    1996-07-01

    Jacobian elliptic travelling wave solutions for a new Hamiltonian amplitude equation determining some instabilities of modulated wave train are obtained. By a mere variation of the Jacobian elliptic parameter k 2 from zero to one, these solutions are transformed from a trivial one to the known solitary wave solutions. (author). 9 refs

  1. Smooth and non-smooth travelling waves in a nonlinearly dispersive Boussinesq equation

    International Nuclear Information System (INIS)

    Shen Jianwei; Xu Wei; Lei Youming

    2005-01-01

    The dynamical behavior and special exact solutions of nonlinear dispersive Boussinesq equation (B(m,n) equation), u tt -u xx -a(u n ) xx +b(u m ) xxxx =0, is studied by using bifurcation theory of dynamical system. As a result, all possible phase portraits in the parametric space for the travelling wave system, solitary wave, kink and anti-kink wave solutions and uncountably infinite many smooth and non-smooth periodic wave solutions are obtained. It can be shown that the existence of singular straight line in the travelling wave system is the reason why smooth waves converge to cusp waves, finally. When parameter are varied, under different parametric conditions, various sufficient conditions guarantee the existence of the above solutions are given

  2. Nonlinear evolution equations for waves in random media

    International Nuclear Information System (INIS)

    Pelinovsky, E.; Talipova, T.

    1994-01-01

    The scope of this paper is to highlight the main ideas of asymptotical methods applying in modern approaches of description of nonlinear wave propagation in random media. We start with the discussion of the classical conception of ''mean field''. Then an exactly solvable model describing nonlinear wave propagation in the medium with fluctuating parameters is considered in order to demonstrate that the ''mean field'' method is not correct. We develop new asymptotic procedures of obtaining the nonlinear evolution equations for the wave fields in random media. (author). 16 refs

  3. CFD Simulations of Floating Point Absorber Wave Energy Converter Arrays Subjected to Regular Waves

    Directory of Open Access Journals (Sweden)

    Brecht Devolder

    2018-03-01

    Full Text Available In this paper we use the Computational Fluid Dynamics (CFD toolbox OpenFOAM to perform numerical simulations of multiple floating point absorber wave energy converters (WECs arranged in a geometrical array configuration inside a numerical wave tank (NWT. The two-phase Navier-Stokes fluid solver is coupled with a motion solver to simulate the hydrodynamic flow field around the WECs and the wave-induced rigid body heave motion of each WEC within the array. In this study, the numerical simulations of a single WEC unit are extended to multiple WECs and the complexity of modelling individual floating objects close to each other in an array layout is tackled. The NWT is validated for fluid-structure interaction (FSI simulations by using experimental measurements for an array of two, five and up to nine heaving WECs subjected to regular waves. The validation is achieved by using mathematical models to include frictional forces observed during the experimental tests. For all the simulations presented, a good agreement is found between the numerical and the experimental results for the WECs’ heave motions, the surge forces on the WECs and the perturbed wave field around the WECs. As a result, our coupled CFD–motion solver proves to be a suitable and accurate toolbox for the study of fluid-structure interaction problems of WEC arrays.

  4. Global smooth solutions of 3-D null-form wave equations in exterior domains with Neumann boundary conditions

    Science.gov (United States)

    Jun, Li; Huicheng, Yin

    2018-05-01

    The paper is devoted to investigating long time behavior of smooth small data solutions to 3-D quasilinear wave equations outside of compact convex obstacles with Neumann boundary conditions. Concretely speaking, when the surface of a 3-D compact convex obstacle is smooth and the quasilinear wave equation fulfills the null condition, we prove that the smooth small data solution exists globally provided that the Neumann boundary condition on the exterior domain is given. One of the main ingredients in the current paper is the establishment of local energy decay estimates of the solution itself. As an application of the main result, the global stability to 3-D static compressible Chaplygin gases in exterior domain is shown under the initial irrotational perturbation with small amplitude.

  5. (3 + 1)-dimensional cylindrical Korteweg-de Vries equation for nonextensive dust acoustic waves: Symbolic computation and exact solutions

    International Nuclear Information System (INIS)

    Guo Shimin; Wang Hongli; Mei Liquan

    2012-01-01

    By combining the effects of bounded cylindrical geometry, azimuthal and axial perturbations, the nonlinear dust acoustic waves (DAWs) in an unmagnetized plasma consisting of negatively charged dust grains, nonextensive ions, and nonextensive electrons are studied in this paper. Using the reductive perturbation method, a (3 + 1)-dimensional variable-coefficient cylindrical Korteweg-de Vries (KdV) equation describing the nonlinear propagation of DAWs is derived. Via the homogeneous balance principle, improved F-expansion technique and symbolic computation, the exact traveling and solitary wave solutions of the KdV equation are presented in terms of Jacobi elliptic functions. Moreover, the effects of the plasma parameters on the solitary wave structures are discussed in detail. The obtained results could help in providing a good fit between theoretical analysis and real applications in space physics and future laboratory plasma experiments where long-range interactions are present.

  6. A Regularized Approach for Solving Magnetic Differential Equations and a Revised Iterative Equilibrium Algorithm

    International Nuclear Information System (INIS)

    Hudson, S.R.

    2010-01-01

    A method for approximately solving magnetic differential equations is described. The approach is to include a small diffusion term to the equation, which regularizes the linear operator to be inverted. The extra term allows a 'source-correction' term to be defined, which is generally required in order to satisfy the solvability conditions. The approach is described in the context of computing the pressure and parallel currents in the iterative approach for computing magnetohydrodynamic equilibria.

  7. Generating asymptotically plane wave spacetimes

    International Nuclear Information System (INIS)

    Hubeny, Veronika E.; Rangamani, Mukund

    2003-01-01

    In an attempt to study asymptotically plane wave spacetimes which admit an event horizon, we find solutions to vacuum Einstein's equations in arbitrary dimension which have a globally null Killing field and rotational symmetry. We show that while such solutions can be deformed to include ones which are asymptotically plane wave, they do not posses a regular event horizon. If we allow for additional matter, such as in supergravity theories, we show that it is possible to have extremal solutions with globally null Killing field, a regular horizon, and which, in addition, are asymptotically plane wave. In particular, we deform the extremal M2-brane solution in 11-dimensional supergravity so that it behaves asymptotically as a 10-dimensional vacuum plane wave times a real line. (author)

  8. Mathematical investigation of tsunami-like long waves interaction with submerge dike of different thickness

    Science.gov (United States)

    Zhiltsov, Konstantin; Kostyushin, Kirill; Kagenov, Anuar; Tyryshkin, Ilya

    2017-11-01

    This paper presents a mathematical investigation of the interaction of a long tsunami-type wave with a submerge dike. The calculations were performed by using the freeware package OpenFOAM. Unsteady two-dimensional Navier-Stokes equations were used for mathematical modeling of incompressible two-phase medium. The Volume of Fluid (VOF) method is used to capture the free surface of a liquid. The effects caused by long wave of defined amplitude motion through a submerged dike of varying thickness were discussed in detail. Numerical results show that after wave passing through the barrier, multiple vortex structures were formed behind. Intensity of vortex depended on the size of the barrier. The effectiveness of the submerge barrier was estimated by evaluating the wave reflection and transmission coefficients using the energy integral method. Then, the curves of the dependences of the reflection and transmission coefficients were obtained for the interaction of waves with the dike. Finally, it was confirmed that the energy of the wave could be reduced by more than 50% when it passed through the barrier.

  9. Finite element and discontinuous Galerkin methods for transient wave equations

    CERN Document Server

    Cohen, Gary

    2017-01-01

    This monograph presents numerical methods for solving transient wave equations (i.e. in time domain). More precisely, it provides an overview of continuous and discontinuous finite element methods for these equations, including their implementation in physical models, an extensive description of 2D and 3D elements with different shapes, such as prisms or pyramids, an analysis of the accuracy of the methods and the study of the Maxwell’s system and the important problem of its spurious free approximations. After recalling the classical models, i.e. acoustics, linear elastodynamics and electromagnetism and their variational formulations, the authors present a wide variety of finite elements of different shapes useful for the numerical resolution of wave equations. Then, they focus on the construction of efficient continuous and discontinuous Galerkin methods and study their accuracy by plane wave techniques and a priori error estimates. A chapter is devoted to the Maxwell’s system and the important problem ...

  10. Detecting breast microcalcifications using super-resolution and wave-equation ultrasound imaging: a numerical phantom study

    Energy Technology Data Exchange (ETDEWEB)

    Huang, Lianjie [Los Alamos National Laboratory; Simonetti, Francesco [IMPERIAL COLLEGE LONDON; Huthwaite, Peter [IMPERIAL COLLEGE LONDON; Rosenberg, Robert [UNM; Williamson, Michael [UNM

    2010-01-01

    Ultrasound image resolution and quality need to be significantly improved for breast microcalcification detection. Super-resolution imaging with the factorization method has recently been developed as a promising tool to break through the resolution limit of conventional imaging. In addition, wave-equation reflection imaging has become an effective method to reduce image speckles by properly handling ultrasound scattering/diffraction from breast heterogeneities during image reconstruction. We explore the capabilities of a novel super-resolution ultrasound imaging method and a wave-equation reflection imaging scheme for detecting breast microcalcifications. Super-resolution imaging uses the singular value decomposition and a factorization scheme to achieve an image resolution that is not possible for conventional ultrasound imaging. Wave-equation reflection imaging employs a solution to the acoustic-wave equation in heterogeneous media to backpropagate ultrasound scattering/diffraction waves to scatters and form images of heterogeneities. We construct numerical breast phantoms using in vivo breast images, and use a finite-difference wave-equation scheme to generate ultrasound data scattered from inclusions that mimic microcalcifications. We demonstrate that microcalcifications can be detected at full spatial resolution using the super-resolution ultrasound imaging and wave-equation reflection imaging methods.

  11. Singular pontentials and analytic regularization in classical Yang-Mills equations

    International Nuclear Information System (INIS)

    Bollini, C.G.; Giambiagi, J.J.; Tiomno, J.

    1978-11-01

    The class of instanton solutions with 'extension' parameter lambda 2 positive is extended to lambda 2 negative. The nature of the singular sphere of radius 'lambda' is analized in the light of the analytical regularization method. This leads to well defined solutions of the Yang-Mills equations. Some of them are sourceless ('+-io' and 'Vp'), others correspond to currents concentrated on the sphere of singularity ('+' and '-'). Although the equations are non-linear, the 'Vp' solution turns out to be real part of the '+-io' solutions. The anzats of t'Hooft for the superposition of instantons is used to sum the contributions corresponding to lambda 2 with positive and negative signs. A subsequent limiting process allows then the construction of solutions of the 'multipole' type. The general situation of potentials having a denominator D, with a corresponding surface of singularity at D=0, is also considered in the same light [pt

  12. An Unconditionally Stable Method for Solving the Acoustic Wave Equation

    Directory of Open Access Journals (Sweden)

    Zhi-Kai Fu

    2015-01-01

    Full Text Available An unconditionally stable method for solving the time-domain acoustic wave equation using Associated Hermit orthogonal functions is proposed. The second-order time derivatives in acoustic wave equation are expanded by these orthogonal basis functions. By applying Galerkin temporal testing procedure, the time variable can be eliminated from the calculations. The restriction of Courant-Friedrichs-Levy (CFL condition in selecting time step for analyzing thin layer can be avoided. Numerical results show the accuracy and the efficiency of the proposed method.

  13. Existence, regularity and representation of solutions of time fractional wave equations

    Directory of Open Access Journals (Sweden)

    Valentin Keyantuo

    2017-09-01

    Full Text Available We study the solvability of the fractional order inhomogeneous Cauchy problem $$ \\mathbb{D}_t^\\alpha u(t=Au(t+f(t, \\quad t>0,\\;1<\\alpha\\le 2, $$ where A is a closed linear operator in some Banach space X and $f:[0,\\infty\\to X$ a given function. Operator families associated with this problem are defined and their regularity properties are investigated. In the case where A is a generator of a $\\beta$-times integrated cosine family $(C_\\beta(t$, we derive explicit representations of mild and classical solutions of the above problem in terms of the integrated cosine family. We include applications to elliptic operators with Dirichlet, Neumann or Robin type boundary conditions on $L^p$-spaces and on the space of continuous functions.

  14. Wave Functions for Time-Dependent Dirac Equation under GUP

    Science.gov (United States)

    Zhang, Meng-Yao; Long, Chao-Yun; Long, Zheng-Wen

    2018-04-01

    In this work, the time-dependent Dirac equation is investigated under generalized uncertainty principle (GUP) framework. It is possible to construct the exact solutions of Dirac equation when the time-dependent potentials satisfied the proper conditions. In (1+1) dimensions, the analytical wave functions of the Dirac equation under GUP have been obtained for the two kinds time-dependent potentials. Supported by the National Natural Science Foundation of China under Grant No. 11565009

  15. Multi-wave solutions of the space–time fractional Burgers and Sharma–Tasso–Olver equations

    OpenAIRE

    Emad A.-B. Abdel-Salam; Gamal F. Hassan

    2016-01-01

    Based on the improved generalized exp-function method, the space–time fractional Burgers and Sharma–Tasso–Olver equations were studied. The single-wave, double-wave, three-wave and four-wave solution discussed. With the best of our knowledge, some of the results are obtained for the first time. The improved generalized exp-function method can be applied to other fractional differential equations.

  16. Dirac equation and optical wave propagation in one dimension

    Energy Technology Data Exchange (ETDEWEB)

    Gonzalez, Gabriel [Catedras CONACYT, Universidad Autonoma de San Luis Potosi (Mexico); Coordinacion para la Innovacion y la Aplicacion de la Ciencia y la Tecnologia, Universidad Autonoma de San Luis Potosi (Mexico)

    2018-02-15

    We show that the propagation of transverse electric (TE) polarized waves in one-dimensional inhomogeneous settings can be written in the form of the Dirac equation in one space dimension with a Lorentz scalar potential, and consequently perform photonic simulations of the Dirac equation in optical structures. In particular, we propose how the zero energy state of the Jackiw-Rebbi model can be generated in an optical set-up by controlling the refractive index landscape, where TE-polarized waves mimic the Dirac particles and the soliton field can be tuned by adjusting the refractive index. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  17. Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

    Science.gov (United States)

    Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue

    2018-01-01

    This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0 . Furthermore, we prove the global existence and uniqueness of C^{α ,β } -solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1 -space. The exponential convergence rate is also derived.

  18. Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

    Science.gov (United States)

    Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue

    2018-06-01

    This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0. Furthermore, we prove the global existence and uniqueness of C^{α ,β }-solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1-space. The exponential convergence rate is also derived.

  19. Quadratic algebras in the noncommutative integration method of wave equation

    International Nuclear Information System (INIS)

    Varaksin, O.L.

    1995-01-01

    The paper deals with the investigation of applications of the method of noncommutative integration of linear differential equations by partial derivatives. Nontrivial example was taken for integration of three-dimensions wave equation with the use of non-Abelian quadratic algebras

  20. Fifth-order amplitude equation for traveling waves in isothermal double diffusive convection

    International Nuclear Information System (INIS)

    Mendoza, S.; Becerril, R.

    2009-01-01

    Third-order amplitude equations for isothermal double diffusive convection are known to hold the tricritical condition all along the oscillatory branch, predicting that stable traveling waves exist Only at the onset of the instability. In order to properly describe stable traveling waves, we perform a fifth-order calculation and present explicitly the corresponding amplitude equation.

  1. Analytic Approximations for Soliton Solutions of Short-Wave Models for Camassa-Holm and Degasperis-Procesi Equations

    International Nuclear Information System (INIS)

    Yang Pei; Li Zhibin; Chen Yong

    2010-01-01

    In this paper, the short-wave model equations are investigated, which are associated with the Camassa-Holm (CH) and Degasperis-Procesi (DP) shallow-water wave equations. Firstly, by means of the transformation of the independent variables and the travelling wave transformation, the partial differential equation is reduced to an ordinary differential equation. Secondly, the equation is solved by homotopy analysis method. Lastly, by the transformations back to the original independent variables, the solution of the original partial differential equation is obtained. The two types of solutions of the short-wave models are obtained in parametric form, one is one-cusp soliton for the CH equation while the other one is one-loop soliton for the DP equation. The approximate analytic solutions expressed by a series of exponential functions agree well with the exact solutions. It demonstrates the validity and great potential of homotopy analysis method for complicated nonlinear solitary wave problems. (general)

  2. Nonlinear and linear wave equations for propagation in media with frequency power law losses

    Science.gov (United States)

    Szabo, Thomas L.

    2003-10-01

    The Burgers, KZK, and Westervelt wave equations used for simulating wave propagation in nonlinear media are based on absorption that has a quadratic dependence on frequency. Unfortunately, most lossy media, such as tissue, follow a more general frequency power law. The authors first research involved measurements of loss and dispersion associated with a modification to Blackstock's solution to the linear thermoviscous wave equation [J. Acoust. Soc. Am. 41, 1312 (1967)]. A second paper by Blackstock [J. Acoust. Soc. Am. 77, 2050 (1985)] showed the loss term in the Burgers equation for plane waves could be modified for other known instances of loss. The authors' work eventually led to comprehensive time-domain convolutional operators that accounted for both dispersion and general frequency power law absorption [Szabo, J. Acoust. Soc. Am. 96, 491 (1994)]. Versions of appropriate loss terms were developed to extend the standard three nonlinear wave equations to these more general losses. Extensive experimental data has verified the predicted phase velocity dispersion for different power exponents for the linear case. Other groups are now working on methods suitable for solving wave equations numerically for these types of loss directly in the time domain for both linear and nonlinear media.

  3. Some isometrical identities in the wave equation

    Directory of Open Access Journals (Sweden)

    Saburou Saitoh

    1984-01-01

    Full Text Available We consider the usual wave equation utt(x,t=c2uxx(x,t on the real line with some typical initial and boundary conditions. In each case, we establish a natural isometrical identity and inverse formula between the sourse function and the response function.

  4. Multi-wave solutions of the space–time fractional Burgers and Sharma–Tasso–Olver equations

    Directory of Open Access Journals (Sweden)

    Emad A.-B. Abdel-Salam

    2016-03-01

    Full Text Available Based on the improved generalized exp-function method, the space–time fractional Burgers and Sharma–Tasso–Olver equations were studied. The single-wave, double-wave, three-wave and four-wave solution discussed. With the best of our knowledge, some of the results are obtained for the first time. The improved generalized exp-function method can be applied to other fractional differential equations.

  5. Propagation of nonlinear ion acoustic wave with generation of long-wavelength waves

    International Nuclear Information System (INIS)

    Ohsawa, Yukiharu; Kamimura, Tetsuo

    1978-01-01

    The nonlinear propagation of the wave packet of an ion acoustic wave with wavenumber k 0 asymptotically equals k sub(De) (the electron Debye wavenumber) is investigated by computer simulations. From the wave packet of the ion acoustic wave, waves with long wavelengths are observed to be produced within a few periods for the amplitude oscillation of the original wave packet. These waves are generated in the region where the original wave packet exists. Their characteristic wavelength is of the order of the length of the wave packet, and their propagation velocity is almost equal to the ion acoustic speed. The long-wavelength waves thus produced strongly affect the nonlinear evolution of the original wave packet. (auth.)

  6. High Order Numerical Simulation of Waves Using Regular Grids and Non-conforming Interfaces

    Science.gov (United States)

    2013-10-06

    for a homogeneous problem . . . . . . . . . . . . . . . . . 65 6 BEP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 7...Lqu = 0, and Tr u = ξΓ. Finally, we have proved that ξΓ satisfies the BEP if and only if ξΓ = Tr u for which Lq u = 0 [51, 53, 39]. We call equation...2.9) the boundary equation with projection ( BEP ). 2.1.1 Wave Split The solutions to the homogeneous equation Lqu = 0 can be interpreted as incoming

  7. A membrane wave equation for Q.C.D. (SU(infinity))

    International Nuclear Information System (INIS)

    Botelho, L.C.L.

    1988-01-01

    It is proposed a quantum membrane wave functional describing the interaction between a colored SU(N c ) membrane and a quantized Yang-Mills field. Additionally, its associated wave equation in the t'Hooft N c ->infinity limit is deduced. (A.C.A.S.) [pt

  8. Inherent Limitations in Mid-Wave and Long-Wave-IR Upconversion Detector

    DEFF Research Database (Denmark)

    Barh, Ajanta; Tseng, Yu-Pei; Pedersen, Christian

    2017-01-01

    Inherent limitations in terms of optical losses, selection of nonlinear crystal(s), detection efficiency and pumping conditions in mid-wave (3-5 µm) and long-wave (8-12 µm) infrared frequency upconversion modules are investigated in this paper.......Inherent limitations in terms of optical losses, selection of nonlinear crystal(s), detection efficiency and pumping conditions in mid-wave (3-5 µm) and long-wave (8-12 µm) infrared frequency upconversion modules are investigated in this paper....

  9. Singular potentials and analytic regularization in classical Yang-Mills equations

    International Nuclear Information System (INIS)

    Bollini, C.G.; Giambiagi, J.J.; Tiomno, J.

    1978-10-01

    The class of instanton solutions with 'extension' parameter Λ 2 positive is extended to Λ 2 negative. The nature of the singular sphere of radius |Λ| is analized in the light of the analytical regularization method. This leads to well defined solutions of the Yang - Mills equations. Some of them are sourceless ('+- i o' and 'Vp'), others correspond to currents concentrated on the sphere of singularity ('+' and '-'). Although the equations are non-linear, the 'Vp' solutions turns out to be the real part of the '+- i o' solutions. The anzats of t'Hooft for the superposition of instantons is used to sum the contributions corresponding to Λ 2 with positive and negative signs. A subsequent limiting process allows then the construction of solutions of the 'multipole' type. The general situation of potentials having a denominator D, with a corresponding surface of singularity at D=0, is also considered in the same light. (Author) [pt

  10. An arbitrary-order staggered time integrator for the linear acoustic wave equation

    Science.gov (United States)

    Lee, Jaejoon; Park, Hyunseo; Park, Yoonseo; Shin, Changsoo

    2018-02-01

    We suggest a staggered time integrator whose order of accuracy can arbitrarily be extended to solve the linear acoustic wave equation. A strategy to select the appropriate order of accuracy is also proposed based on the error analysis that quantitatively predicts the truncation error of the numerical solution. This strategy not only reduces the computational cost several times, but also allows us to flexibly set the modelling parameters such as the time step length, grid interval and P-wave speed. It is demonstrated that the proposed method can almost eliminate temporal dispersive errors during long term simulations regardless of the heterogeneity of the media and time step lengths. The method can also be successfully applied to the source problem with an absorbing boundary condition, which is frequently encountered in the practical usage for the imaging algorithms or the inverse problems.

  11. Global regularity for a family of 3D models of the axi-symmetric Navier–Stokes equations

    Science.gov (United States)

    Hou, Thomas Y.; Liu, Pengfei; Wang, Fei

    2018-05-01

    We consider a family of three-dimensional models for the axi-symmetric incompressible Navier–Stokes equations. The models are derived by changing the strength of the convection terms in the axisymmetric Navier–Stokes equations written using a set of transformed variables. We prove the global regularity of the family of models in the case that the strength of convection is slightly stronger than that of the original Navier–Stokes equations, which demonstrates the potential stabilizing effect of convection.

  12. Singular solitons and other solutions to a couple of nonlinear wave equations

    International Nuclear Information System (INIS)

    Inc Mustafa; Ulutaş Esma; Biswas Anjan

    2013-01-01

    This paper addresses the extended (G'/G)-expansion method and applies it to a couple of nonlinear wave equations. These equations are modified the Benjamin—Bona—Mahoney equation and the Boussinesq equation. This extended method reveals several solutions to these equations. Additionally, the singular soliton solutions are revealed, for these two equations, with the aid of the ansatz method

  13. Energy-preserving H1-Galerkin schemes for shallow water wave equations with peakon solutions

    International Nuclear Information System (INIS)

    Miyatake, Yuto; Matsuo, Takayasu

    2012-01-01

    New energy-preserving Galerkin schemes for the Camassa–Holm and the Degasperis–Procesi equations which model shallow water waves are presented. The schemes can be implemented only with cheap H 1 elements, which is expected to be sufficient to catch the characteristic peakon solutions. The keys of the derivation are the Hamiltonian structures of the equations and an L 2 -projection technique newly employed in the present Letter to mimic the Hamiltonian structures in a discrete setting, so that the desired energy-preserving property rightly follows. Numerical examples confirm the effectiveness of the schemes. -- Highlights: ► Numerical integration of the Camassa–Holm and Degasperis–Procesi equation. ► New energy-preserving Galerkin schemes for these equations are proposed. ► They can be implemented only with P1 elements. ► They well capture the characteristic peakon solutions over long time. ► The keys are the Hamiltonian structures and L 2 -projection technique.

  14. Control Operator for the Two-Dimensional Energized Wave Equation

    Directory of Open Access Journals (Sweden)

    Sunday Augustus REJU

    2006-07-01

    Full Text Available This paper studies the analytical model for the construction of the two-dimensional Energized wave equation. The control operator is given in term of space and time t independent variables. The integral quadratic objective cost functional is subject to the constraint of two-dimensional Energized diffusion, Heat and a source. The operator that shall be obtained extends the Conjugate Gradient method (ECGM as developed by Hestenes et al (1952, [1]. The new operator enables the computation of the penalty cost, optimal controls and state trajectories of the two-dimensional energized wave equation when apply to the Conjugate Gradient methods in (Waziri & Reju, LEJPT & LJS, Issues 9, 2006, [2-4] to appear in this series.

  15. A dynamical regularization algorithm for solving inverse source problems of elliptic partial differential equations

    Science.gov (United States)

    Zhang, Ye; Gong, Rongfang; Cheng, Xiaoliang; Gulliksson, Mårten

    2018-06-01

    This study considers the inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary data. The unknown source term is to be determined by additional boundary conditions. Unlike the existing methods found in the literature, which usually employ the first-order in time gradient-like system (such as the steepest descent methods) for numerically solving the regularized optimization problem with a fixed regularization parameter, we propose a novel method with a second-order in time dissipative gradient-like system and a dynamical selected regularization parameter. A damped symplectic scheme is proposed for the numerical solution. Theoretical analysis is given for both the continuous model and the numerical algorithm. Several numerical examples are provided to show the robustness of the proposed algorithm.

  16. The wave equation: From eikonal to anti-eikonal approximation

    Directory of Open Access Journals (Sweden)

    Luis Vázquez

    2016-06-01

    Full Text Available When the refractive index changes very slowly compared to the wave-length we may use the eikonal approximation to the wave equation. In the opposite case, when the refractive index highly variates over the distance of one wave-length, we have what can be termed as the anti-eikonal limit. This situation is addressed in this work. The anti-eikonal limit seems to be a relevant tool in the modelling and design of new optical media. Besides, it describes a basic universal behaviour, independent of the actual values of the refractive index and, thus, of the media, for the components of a wave with wave-length much greater than the characteristic scale of the refractive index.

  17. Closed form solutions of two time fractional nonlinear wave equations

    Science.gov (United States)

    Akbar, M. Ali; Ali, Norhashidah Hj. Mohd.; Roy, Ripan

    2018-06-01

    In this article, we investigate the exact traveling wave solutions of two nonlinear time fractional wave equations. The fractional derivatives are described in the sense of conformable fractional derivatives. In addition, the traveling wave solutions are accomplished in the form of hyperbolic, trigonometric, and rational functions involving free parameters. To investigate such types of solutions, we implement the new generalized (G‧ / G) -expansion method. The extracted solutions are reliable, useful and suitable to comprehend the optimal control problems, chaotic vibrations, global and local bifurcations and resonances, furthermore, fission and fusion phenomena occur in solitons, the relativistic energy-momentum relation, scalar electrodynamics, quantum relativistic one-particle theory, electromagnetic interactions etc. The results reveal that the method is very fruitful and convenient for exploring nonlinear differential equations of fractional order treated in theoretical physics.

  18. An interpolation between the wave and diffusion equations through the fractional evolution equations Dirac like

    International Nuclear Information System (INIS)

    Pierantozzi, T.; Vazquez, L.

    2005-01-01

    Through fractional calculus and following the method used by Dirac to obtain his well-known equation from the Klein-Gordon equation, we analyze a possible interpolation between the Dirac and the diffusion equations in one space dimension. We study the transition between the hyperbolic and parabolic behaviors by means of the generalization of the D'Alembert formula for the classical wave equation and the invariance under space and time inversions of the interpolating fractional evolution equations Dirac like. Such invariance depends on the values of the fractional index and is related to the nonlocal property of the time fractional differential operator. For this system of fractional evolution equations, we also find an associated conserved quantity analogous to the Hamiltonian for the classical Dirac case

  19. Differential equation for Alfven ion cyclotron waves in finite-length plasma

    International Nuclear Information System (INIS)

    Watson, D.C.; Fateman, R.J.; Baldwin, D.E.

    1977-01-01

    One finds the fourth-order differential equation describing an Alfven-ion-cyclotron wave propagating along a magnetic field of varying intensity. The equation is self-adjoint and possesses non-trivial turning points. The final form of the equation is checked using MACSYMA, a system for performing algebra on a computer

  20. Quaternion wave equations in curved space-time

    Science.gov (United States)

    Edmonds, J. D., Jr.

    1974-01-01

    The quaternion formulation of relativistic quantum theory is extended to include curvilinear coordinates and curved space-time in order to provide a framework for a unified quantum/gravity theory. Six basic quaternion fields are identified in curved space-time, the four-vector basis quaternions are identified, and the necessary covariant derivatives are obtained. Invariant field equations are derived, and a general invertable coordinate transformation is developed. The results yield a way of writing quaternion wave equations in curvilinear coordinates and curved space-time as well as a natural framework for solving the problem of second quantization for gravity.

  1. New binary travelling-wave periodic solutions for the modified KdV equation

    International Nuclear Information System (INIS)

    Yan Zhenya

    2008-01-01

    In this Letter, the modified Korteweg-de Vries (mKdV) equations with the focusing (+) and defocusing (-) branches are investigated, respectively. Many new types of binary travelling-wave periodic solutions are obtained for the mKdV equation in terms of Jacobi elliptic functions such as sn(ξ,m)cn(ξ,m)dn(ξ,m) and their extensions. Moreover, we analyze asymptotic properties of some solutions. In addition, with the aid of the Miura transformation, we also give the corresponding binary travelling-wave periodic solutions of KdV equation

  2. Low Frequency Waves Detected in a Large Wave Flume under Irregular Waves with Different Grouping Factor and Combination of Regular Waves

    Directory of Open Access Journals (Sweden)

    Luigia Riefolo

    2018-02-01

    Full Text Available This paper describes a set of experiments undertaken at Universitat Politècnica de Catalunya in the large wave flume of the Maritime Engineering Laboratory. The purpose of this study is to highlight the effects of wave grouping and long-wave short-wave combinations regimes on low frequency generations. An eigen-value decomposition has been performed to discriminate low frequencies. In particular, measured eigen modes, determined through the spectral analysis, have been compared with calculated modes by means of eigen analysis. The low frequencies detection appears to confirm the dependence on groupiness of the modal amplitudes generated in the wave flume. Some evidence of the influence of low frequency waves on runup and transport patterns are shown. In particular, the generation and evolution of secondary bedforms are consistent with energy transferred between the standing wave modes.

  3. Wave-equation dispersion inversion of surface waves recorded on irregular topography

    KAUST Repository

    Li, Jing; Schuster, Gerard T.; Lin, Fan-Chi; Alam, Amir

    2017-01-01

    Significant topographic variations will strongly influence the amplitudes and phases of propagating surface waves. Such effects should be taken into account, otherwise the S-velocity model inverted from the Rayleigh dispersion curves will contain significant inaccuracies. We now show that the recently developed wave-equation dispersion inversion (WD) method naturally takes into account the effects of topography to give accurate S-velocity tomograms. Application of topographic WD to demonstrates that WD can accurately invert dispersion curves from seismic data recorded over variable topography. We also apply this method to field data recorded on the crest of mountainous terrain and find with higher resolution than the standard WD tomogram.

  4. Wave-equation dispersion inversion of surface waves recorded on irregular topography

    KAUST Repository

    Li, Jing

    2017-08-17

    Significant topographic variations will strongly influence the amplitudes and phases of propagating surface waves. Such effects should be taken into account, otherwise the S-velocity model inverted from the Rayleigh dispersion curves will contain significant inaccuracies. We now show that the recently developed wave-equation dispersion inversion (WD) method naturally takes into account the effects of topography to give accurate S-velocity tomograms. Application of topographic WD to demonstrates that WD can accurately invert dispersion curves from seismic data recorded over variable topography. We also apply this method to field data recorded on the crest of mountainous terrain and find with higher resolution than the standard WD tomogram.

  5. Regular growth of systems of functions and systems of non-homogeneous convolution equations in convex domains of the complex plane

    International Nuclear Information System (INIS)

    Krivosheev, A S

    2000-01-01

    In this paper we introduce the notion of regular growth for a system of entire functions of finite order and type. This is a direct and natural generalization of the classical completely regular growth of an entire function. We obtain sufficient and necessary conditions for the solubility of a system of non-homogeneous convolution equations in convex domains of the complex plane. These conditions depend on whether the system of Laplace transforms of the analytic functionals that generate the convolution equations has regular growth. In the case of smooth convex domains, these solubility conditions form a criterion

  6. New solutions of the generalized ellipsoidal wave equation

    Directory of Open Access Journals (Sweden)

    Harold Exton

    1999-10-01

    Full Text Available Certain aspects and a contribution to the theory of new forms of solutions of an algebraic form of the generalized ellipsoidal wave equation are deduced by considering the Laplace transform of a soluble system of linear differential equations. An ensuing system of non-linear algebraic equations is shown to be consistent and is numerically implemented by means of the computer algebra package MAPLE V. The main results are presented as series of hypergeometric type of there and four variables which readily lend themselves to numerical handling although this does not indicate all of the detailedanalytic properties of the solutions under consideration.

  7. Solution of wave-like equation based on Haar wavelet

    Directory of Open Access Journals (Sweden)

    Naresh Berwal

    2012-11-01

    Full Text Available Wavelet transform and wavelet analysis are powerful mathematical tools for many problems. Wavelet also can be applied in numerical analysis. In this paper, we apply Haar wavelet method to solve wave-like equation with initial and boundary conditions known. The fundamental idea of Haar wavelet method is to convert the differential equations into a group of algebraic equations, which involves a finite number or variables. The results and graph show that the proposed way is quite reasonable when compared to exact solution.

  8. Analysis of global multiscale finite element methods for wave equations with continuum spatial scales

    KAUST Repository

    Jiang, Lijian; Efendiev, Yalchin; Ginting, Victor

    2010-01-01

    In this paper, we discuss a numerical multiscale approach for solving wave equations with heterogeneous coefficients. Our interest comes from geophysics applications and we assume that there is no scale separation with respect to spatial variables. To obtain the solution of these multiscale problems on a coarse grid, we compute global fields such that the solution smoothly depends on these fields. We present a Galerkin multiscale finite element method using the global information and provide a convergence analysis when applied to solve the wave equations. We investigate the relation between the smoothness of the global fields and convergence rates of the global Galerkin multiscale finite element method for the wave equations. Numerical examples demonstrate that the use of global information renders better accuracy for wave equations with heterogeneous coefficients than the local multiscale finite element method. © 2010 IMACS.

  9. Analysis of global multiscale finite element methods for wave equations with continuum spatial scales

    KAUST Repository

    Jiang, Lijian

    2010-08-01

    In this paper, we discuss a numerical multiscale approach for solving wave equations with heterogeneous coefficients. Our interest comes from geophysics applications and we assume that there is no scale separation with respect to spatial variables. To obtain the solution of these multiscale problems on a coarse grid, we compute global fields such that the solution smoothly depends on these fields. We present a Galerkin multiscale finite element method using the global information and provide a convergence analysis when applied to solve the wave equations. We investigate the relation between the smoothness of the global fields and convergence rates of the global Galerkin multiscale finite element method for the wave equations. Numerical examples demonstrate that the use of global information renders better accuracy for wave equations with heterogeneous coefficients than the local multiscale finite element method. © 2010 IMACS.

  10. On Regularly Varying and History-Dependent Convergence Rates of Solutions of a Volterra Equation with Infinite Memory

    OpenAIRE

    John A. D. Appleby

    2010-01-01

    We consider the rate of convergence to equilibrium of Volterra integrodifferential equations with infinite memory. We show that if the kernel of Volterra operator is regularly varying at infinity, and the initial history is regularly varying at minus infinity, then the rate of convergence to the equilibrium is regularly varying at infinity, and the exact pointwise rate of convergence can be determined in terms of the rate of decay of the kernel and the rate of growth of the initial history. ...

  11. ''Free-space'' boundary conditions for the time-dependent wave equation

    International Nuclear Information System (INIS)

    Lindman, E.L.

    1975-01-01

    Boundary conditions for the discrete wave equation which act like an infinite region of free space in contact with the computational region can be constructed using projection operators. Propagating and evanescent waves coming from within the computational region generate no reflected waves as they cross the boundary. At the same time arbitrary waves may be launched into the computational region. Well known projection operators for one-dimensional waves may be used for this purpose in one dimension. Extensions of these operators to higher dimensions along with numerically efficient approximations to them are described for higher-dimensional problems. The separation of waves into ingoing and outgoing waves inherent in these boundary conditions greatly facilitates diagnostics

  12. Some exact solutions to the potential Kadomtsev-Petviashvili equation and to a system of shallow water wave equations

    International Nuclear Information System (INIS)

    Inan, Ibrahim E.; Kaya, Dogan

    2006-01-01

    In this Letter by considering an improved tanh function method, we found some exact solutions of the potential Kadomtsev-Petviashvili equation. Some exact solutions of the system of the shallow water wave equation were also found

  13. Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria

    International Nuclear Information System (INIS)

    Frieman, E.A.; Chen, L.

    1981-10-01

    A nonlinear gyrokinetic formalism for low-frequency (less than the cyclotron frequency) microscopic electromagnetic perturbations in general magnetic field configurations is developed. The nonlinear equations thus derived are valid in the strong-turbulence regime and contain effects due to finite Larmor radius, plasma inhomogeneities, and magentic field geometries. The specific case of axisymmetric tokamaks is then considered, and a model nonlinear equation is derived for electrostatic drift waves. Also, applying the formalism to the shear Alfven wave heating sceme, it is found that nonlinear ion Landau damping of kinetic shear-Alfven waves is modified, both qualitatively and quantitatively, by the diamagnetic drift effects. In particular, wave energy is found to cascade in wavenumber instead of frequency

  14. Evans functions and bifurcations of nonlinear waves of some nonlinear reaction diffusion equations

    Science.gov (United States)

    Zhang, Linghai

    2017-10-01

    The main purposes of this paper are to accomplish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear system of reaction diffusion equations ut =uxx + α [ βH (u - θ) - u ] - w, wt = ε (u - γw) and to establish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear scalar reaction diffusion equation ut =uxx + α [ βH (u - θ) - u ], under different conditions on the model constants. To establish the bifurcation for the system, we will study the existence and instability of a standing pulse solution if 0 1; the existence and instability of two standing wave fronts if 2 (1 + αγ) θ = αβγ and 0 traveling wave front as well as the existence and instability of a standing pulse solution if 0 traveling wave front as well as the existence and instability of an upside down standing pulse solution if 0 traveling wave back of the nonlinear scalar reaction diffusion equation ut =uxx + α [ βH (u - θ) - u ] -w0, where w0 = α (β - 2 θ) > 0 is a positive constant, if 0 motivation to study the existence, stability, instability and bifurcations of the nonlinear waves is to study the existence and stability/instability of infinitely many fast/slow multiple traveling pulse solutions of the nonlinear system of reaction diffusion equations. The existence and stability of infinitely many fast multiple traveling pulse solutions are of great interests in mathematical neuroscience.

  15. On the exact solutions of high order wave equations of KdV type (I)

    Science.gov (United States)

    Bulut, Hasan; Pandir, Yusuf; Baskonus, Haci Mehmet

    2014-12-01

    In this paper, by means of a proper transformation and symbolic computation, we study high order wave equations of KdV type (I). We obtained classification of exact solutions that contain soliton, rational, trigonometric and elliptic function solutions by using the extended trial equation method. As a result, the motivation of this paper is to utilize the extended trial equation method to explore new solutions of high order wave equation of KdV type (I). This method is confirmed by applying it to this kind of selected nonlinear equations.

  16. Hybrid resonance and long-time asymptotic of the solution to Maxwell's equations

    Energy Technology Data Exchange (ETDEWEB)

    Després, Bruno, E-mail: despres@ann.jussieu.fr [Laboratory Jacques Louis Lions, University Pierre et Marie Curie, Paris VI, Boîte courrier 187, 75252 Paris Cedex 05 (France); Weder, Ricardo, E-mail: weder@unam.mx [Departamento de Física Matemática, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Apartado Postal 20-126, DF 01000 (Mexico)

    2016-03-22

    We study the long-time asymptotic of the solutions to Maxwell's equation in the case of an upper-hybrid resonance in the cold plasma model. We base our analysis in the transfer to the time domain of the recent results of B. Després, L.M. Imbert-Gérard and R. Weder (2014) [15], where the singular solutions to Maxwell's equations in the frequency domain were constructed by means of a limiting absorption principle and a formula for the heating of the plasma in the limit of vanishing collision frequency was obtained. Currently there is considerable interest in these problems, in particular, because upper-hybrid resonances are a possible scenario for the heating of plasmas, and since they can be a model for the diagnostics involving wave scattering in plasmas. - Highlights: • The upper-hybrid resonance in the cold plasma model is considered. • The long-time asymptotic of the solutions to Maxwell's equations is studied. • A method based in a singular limiting absorption principle is proposed.

  17. On "new travelling wave solutions" of the KdV and the KdV-Burgers equations

    NARCIS (Netherlands)

    Kudryashov, Nikolai A.

    The Korteweg-de Vries and the Korteweg-de Vries-Burgers equations are considered. Using the travelling wave the general solutions of these equations are presented. "New travelling wave solutions" of the KdV and the KdV-Burgers equations by Wazzan [Wazzan L Commun Nonlinear Sci Numer Simulat

  18. Rogue waves and rational solutions of a (3+1)-dimensional nonlinear evolution equation

    International Nuclear Information System (INIS)

    Zhaqilao,

    2013-01-01

    A simple symbolic computation approach for finding the rogue waves and rational solutions to the nonlinear evolution equation is proposed. It turns out that many rational solutions with real and complex forms of a (3+1)-dimensional nonlinear evolution equation are obtained. Some features of rogue waves and rational solutions are graphically discussed. -- Highlights: •A simple symbolic computation approach for finding the rational solutions to the NEE is proposed. •Some rogue waves and rational solutions with real and complex forms of a (3+1)-D NEE are obtained. •Some features of rogue waves are graphically discussed

  19. Rogue waves and rational solutions of a (3+1)-dimensional nonlinear evolution equation

    Energy Technology Data Exchange (ETDEWEB)

    Zhaqilao,, E-mail: zhaqilao@imnu.edu.cn

    2013-12-06

    A simple symbolic computation approach for finding the rogue waves and rational solutions to the nonlinear evolution equation is proposed. It turns out that many rational solutions with real and complex forms of a (3+1)-dimensional nonlinear evolution equation are obtained. Some features of rogue waves and rational solutions are graphically discussed. -- Highlights: •A simple symbolic computation approach for finding the rational solutions to the NEE is proposed. •Some rogue waves and rational solutions with real and complex forms of a (3+1)-D NEE are obtained. •Some features of rogue waves are graphically discussed.

  20. Spinor-electron wave guided modes in coupled quantum wells structures by solving the Dirac equation

    International Nuclear Information System (INIS)

    Linares, Jesus; Nistal, Maria C.

    2009-01-01

    A quantum analysis based on the Dirac equation of the propagation of spinor-electron waves in coupled quantum wells, or equivalently coupled electron waveguides, is presented. The complete optical wave equations for Spin-Up (SU) and Spin-Down (SD) spinor-electron waves in these electron guides couplers are derived from the Dirac equation. The relativistic amplitudes and dispersion equations of the spinor-electron wave-guided modes in a planar quantum coupler formed by two coupled quantum wells, or equivalently by two coupled slab electron waveguides, are exactly derived. The main outcomes related to the spinor modal structure, such as the breaking of the non-relativistic degenerate spin states, the appearance of phase shifts associated with the spin polarization and so on, are shown.

  1. Scalar evolution equations for shear waves in incompressible solids: a simple derivation of the Z, ZK, KZK and KP equations

    KAUST Repository

    Destrade, M.

    2010-12-08

    We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy-Green strain). However, we show that the Z equation cannot be a scalar equation for the propagation of two-dimensional shear waves in general elastic materials (with strain energy depending on the first and second principal invariants of strain). Then, we introduce dispersive and dissipative terms to deduce the scalar Kadomtsev-Petviashvili (KP), Zabolotskaya-Khokhlov (ZK) and Khokhlov- Zabolotskaya-Kuznetsov (KZK) equations of incompressible solid mechanics. © 2010 The Royal Society.

  2. Scalar evolution equations for shear waves in incompressible solids: a simple derivation of the Z, ZK, KZK and KP equations

    KAUST Repository

    Destrade, M.; Goriely, A.; Saccomandi, G.

    2010-01-01

    We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy-Green strain). However, we show that the Z equation cannot be a scalar equation for the propagation of two-dimensional shear waves in general elastic materials (with strain energy depending on the first and second principal invariants of strain). Then, we introduce dispersive and dissipative terms to deduce the scalar Kadomtsev-Petviashvili (KP), Zabolotskaya-Khokhlov (ZK) and Khokhlov- Zabolotskaya-Kuznetsov (KZK) equations of incompressible solid mechanics. © 2010 The Royal Society.

  3. Ion Acceleration in Plasmas with Alfven Waves

    International Nuclear Information System (INIS)

    Kolesnychenko, O.Ya.; Lutsenko, V.V.; White, R.B.

    2005-01-01

    Effects of elliptically polarized Alfven waves on thermal ions are investigated. Both regular oscillations and stochastic motion of the particles are observed. It is found that during regular oscillations the energy of the thermal ions can reach magnitudes well exceeding the plasma temperature, the effect being largest in low-beta plasmas (beta is the ratio of the plasma pressure to the magnetic field pressure). Conditions of a low stochasticity threshold are obtained. It is shown that stochasticity can arise even for waves propagating along the magnetic field provided that the frequency spectrum is non-monochromatic. The analysis carried out is based on equations derived by using a Lagrangian formalism. A code solving these equations is developed. Steady-state perturbations and perturbations with the amplitude slowly varying in time are considered

  4. Electromagnetic wave propagation over an inhomogeneous flat earth (two-dimensional integral equation formulation)

    International Nuclear Information System (INIS)

    de Jong, G.

    1975-01-01

    With the aid of a two-dimensional integral equation formulation, the ground wave propagation of electromagnetic waves transmitted by a vertical electric dipole over an inhomogeneous flat earth is investigated. For the configuration in which a ground wave is propagating across an ''island'' on a flat earth, the modulus and argument of the attenuation function have been computed. The results for the two-dimensional treatment are significantly more accurate in detail than the calculations using a one-dimensional integral equation

  5. Solitons and cnoidal waves of the Klein–Gordon–Zakharov equation ...

    Indian Academy of Sciences (India)

    In (3), κ represents the wave number of the soliton while ω represents ... integration constant to be zero, since the search is for soliton solutions only, gives ..... and also using relations (3)–(5) gives the following rational travelling wave ... In future, the plan is to study the numerical simulations for this equation along with.

  6. Scattering for wave equations with dissipative terms in layered media

    Directory of Open Access Journals (Sweden)

    Mitsuteru Kadowaki

    2011-05-01

    Full Text Available In this article, we show the existence of scattering solutions to wave equations with dissipative terms in layered media. To analyze the wave propagation in layered media, it is necessary to handle singular points called thresholds in the spectrum. Our main tools are Kato's smooth perturbation theory and some approximate operators.

  7. Variable coefficient Korteweg-de Vries equations and travelling waves in an inhomogeneous medium

    International Nuclear Information System (INIS)

    Baby, B.V.

    1987-04-01

    The well-known Korteweg-de Vries equations with the coefficients as two arbitrary functions of the time variable, is studied in this paper. The Painleve property analysis provides the conditions on the two variable coefficients, in order to form the Lax pairs associated with this equation. The similarity analysis shows the non-existence of travelling wave solutions when the equation has variable coefficients. These results are used to show the non-existence of travelling waves in an inhomogeneous medium. (author). 33 refs

  8. A consistent formulation of wave propagation and conversion in low aspect ratio tokamaks with non-circular cross section

    International Nuclear Information System (INIS)

    Cuperman, S.; Bruma, C.; Komoshvili, K.

    1999-01-01

    The authors developed a consistent formalism for the full wave equation, appropriate for the study of propagation, absorption and wave conversion of externally launched waves in strongly toroidal, spherical tokamaks with non-circular cross-section. This includes also the formulation of rigorous regularity, boundary, gauge and periodicity conditions suitable for the exact solution of the wave equation for such devices

  9. Computation of High-Frequency Waves with Random Uncertainty

    KAUST Repository

    Malenova, Gabriela

    2016-01-06

    We consider the forward propagation of uncertainty in high-frequency waves, described by the second order wave equation with highly oscillatory initial data. The main sources of uncertainty are the wave speed and/or the initial phase and amplitude, described by a finite number of random variables with known joint probability distribution. We propose a stochastic spectral asymptotic method [1] for computing the statistics of uncertain output quantities of interest (QoIs), which are often linear or nonlinear functionals of the wave solution and its spatial/temporal derivatives. The numerical scheme combines two techniques: a high-frequency method based on Gaussian beams [2, 3], a sparse stochastic collocation method [4]. The fast spectral convergence of the proposed method depends crucially on the presence of high stochastic regularity of the QoI independent of the wave frequency. In general, the high-frequency wave solutions to parametric hyperbolic equations are highly oscillatory and non-smooth in both physical and stochastic spaces. Consequently, the stochastic regularity of the QoI, which is a functional of the wave solution, may in principle below and depend on frequency. In the present work, we provide theoretical arguments and numerical evidence that physically motivated QoIs based on local averages of |uE|2 are smooth, with derivatives in the stochastic space uniformly bounded in E, where uE and E denote the highly oscillatory wave solution and the short wavelength, respectively. This observable related regularity makes the proposed approach more efficient than current asymptotic approaches based on Monte Carlo sampling techniques.

  10. A delay differential equation model of follicle waves in women.

    Science.gov (United States)

    Panza, Nicole M; Wright, Andrew A; Selgrade, James F

    2016-01-01

    This article presents a mathematical model for hormonal regulation of the menstrual cycle which predicts the occurrence of follicle waves in normally cycling women. Several follicles of ovulatory size that develop sequentially during one menstrual cycle are referred to as follicle waves. The model consists of 13 nonlinear, delay differential equations with 51 parameters. Model simulations exhibit a unique stable periodic cycle and this menstrual cycle accurately approximates blood levels of ovarian and pituitary hormones found in the biological literature. Numerical experiments illustrate that the number of follicle waves corresponds to the number of rises in pituitary follicle stimulating hormone. Modifications of the model equations result in simulations which predict the possibility of two ovulations at different times during the same menstrual cycle and, hence, the occurrence of dizygotic twins via a phenomenon referred to as superfecundation. Sensitive parameters are identified and bifurcations in model behaviour with respect to parameter changes are discussed. Studying follicle waves may be helpful for improving female fertility and for understanding some aspects of female reproductive ageing.

  11. Visco-acoustic wave-equation traveltime inversion and its sensitivity to attenuation errors

    KAUST Repository

    Yu, Han

    2018-02-23

    A visco-acoustic wave-equation traveltime inversion method is presented that inverts for the shallow subsurface velocity distribution. Similar to the classical wave equation traveltime inversion, this method finds the velocity model that minimizes the squared sum of the traveltime residuals. Even though, wave-equation traveltime inversion can partly avoid the cycle skipping problem, a good initial velocity model is required for the inversion to converge to a reasonable tomogram with different attenuation profiles. When Q model is far away from the real model, the final tomogram is very sensitive to the starting velocity model. Nevertheless, a minor or moderate perturbation of the Q model from the true one does not strongly affect the inversion if the low wavenumber information of the initial velocity model is mostly correct. These claims are validated with numerical tests on both the synthetic and field data sets.

  12. Visco-acoustic wave-equation traveltime inversion and its sensitivity to attenuation errors

    Science.gov (United States)

    Yu, Han; Chen, Yuqing; Hanafy, Sherif M.; Huang, Jiangping

    2018-04-01

    A visco-acoustic wave-equation traveltime inversion method is presented that inverts for the shallow subsurface velocity distribution. Similar to the classical wave equation traveltime inversion, this method finds the velocity model that minimizes the squared sum of the traveltime residuals. Even though, wave-equation traveltime inversion can partly avoid the cycle skipping problem, a good initial velocity model is required for the inversion to converge to a reasonable tomogram with different attenuation profiles. When Q model is far away from the real model, the final tomogram is very sensitive to the starting velocity model. Nevertheless, a minor or moderate perturbation of the Q model from the true one does not strongly affect the inversion if the low wavenumber information of the initial velocity model is mostly correct. These claims are validated with numerical tests on both the synthetic and field data sets.

  13. Instability of traveling waves of the convective-diffusive Cahn-Hilliard equation

    International Nuclear Information System (INIS)

    Gao Hongjun; Liu Changchun

    2004-01-01

    In this paper we study the instability of the traveling waves of the convective-diffusive Cahn-Hilliard equation. We prove that it is nonlinearly unstable under H 2 perturbations, for some traveling wave solution that is asymptotic to a constant as x→∞

  14. A comparative study of diffraction of shallow-water waves by high-level IGN and GN equations

    Energy Technology Data Exchange (ETDEWEB)

    Zhao, B.B. [College of Shipbuilding Engineering, Harbin Engineering University, 150001 Harbin (China); Ertekin, R.C. [Department of Ocean and Resources Engineering, University of Hawai' i, Honolulu, HI 96822 (United States); College of Shipbuilding Engineering, Harbin Engineering University, 150001 Harbin (China); Duan, W.Y., E-mail: duanwenyangheu@hotmail.com [College of Shipbuilding Engineering, Harbin Engineering University, 150001 Harbin (China)

    2015-02-15

    This work is on the nonlinear diffraction analysis of shallow-water waves, impinging on submerged obstacles, by two related theories, namely the classical Green–Naghdi (GN) equations and the Irrotational Green–Naghdi (IGN) equations, both sets of equations being at high levels and derived for incompressible and inviscid flows. Recently, the high-level Green–Naghdi equations have been applied to some wave transformation problems. The high-level IGN equations have also been used in the last decade to study certain wave propagation problems. However, past works on these theories used different numerical methods to solve these nonlinear and unsteady sets of differential equations and at different levels. Moreover, different physical problems have been solved in the past. Therefore, it has not been possible to understand the differences produced by these two sets of theories and their range of applicability so far. We are thus motivated to make a direct comparison of the results produced by these theories by use of the same numerical method to solve physically the same wave diffraction problems. We focus on comparing these two theories by using similar codes; only the equations used are different but other parts of the codes, such as the wave-maker, damping zone, discretion method, matrix solver, etc., are exactly the same. This way, we eliminate many potential sources of differences that could be produced by the solution of different equations. The physical problems include the presence of various submerged obstacles that can be used for example as breakwaters or to represent the continental shelf. A numerical wave tank is created by placing a wavemaker on one end and a wave absorbing beach on the other. The nonlinear and unsteady sets of differential equations are solved by the finite-difference method. The results are compared with different equations as well as with the available experimental data.

  15. Numerical Simulation of Freak Waves Based on the Four-Order Nonlinear Schr(o)dinger Equation

    Institute of Scientific and Technical Information of China (English)

    ZHANG Yun-qiu; ZHANG Ning-chuan; PEI Yu-guo

    2007-01-01

    A numerical wave model based on the modified four-order nonlinear Schrodinger (NLS) equation in deep water is developed to simulate freak waves. A standard split-step, pseudo-spectral method is used to solve NLS equation. The validation of the model is firstly verified, and then the simulation of freak waves is performed by changing sideband conditions. Results show that freak waves entirely consistent with the definition in the evolution of wave trains are obtained. The possible occurrence mechanism of freak waves is discussed and the relevant characteristics are also analyzed.

  16. NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION

    OpenAIRE

    Liu, F.; Meerschaert, M.M.; McGough, R.J.; Zhuang, P.; Liu, Q.

    2013-01-01

    In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and technique...

  17. ''Localized'' tachyonic wavelet-solutions of the wave equation

    International Nuclear Information System (INIS)

    Barut, A.O.; Chandola, H.C.

    1993-05-01

    Localized-nonspreading, wavelet-solutions of the wave equation □φ=0 with group velocity v>c and phase velocity u=c 2 /v< c are constructed explicitly by two different methods. Some recent experiments seem to find evidence for superluminal group velocities. (author). 7 refs, 2 figs

  18. New exact travelling wave solutions for the generalized nonlinear Schroedinger equation with a source

    International Nuclear Information System (INIS)

    Abdou, M.A.

    2008-01-01

    The generalized F-expansion method with a computerized symbolic computation is used for constructing a new exact travelling wave solutions for the generalized nonlinear Schrodinger equation with a source. As a result, many exact travelling wave solutions are obtained which include new periodic wave solution, trigonometric function solutions and rational solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in physics

  19. On the evolution of perturbations to solutions of the Kadomtsev-Petviashvilli equation using the Benney-Luke equation

    International Nuclear Information System (INIS)

    Ablowitz, Mark J; Curtis, Christopher W

    2011-01-01

    The Benney-Luke equation, which arises as a long wave asymptotic approximation of water waves, contains the Kadomtsev-Petviashvilli (KP) equation as a leading-order maximal balanced approximation. The question analyzed is how the Benney-Luke equation modifies the so-called web solutions of the KP equation. It is found that the Benney-Luke equation introduces dispersive radiation which breaks each of the symmetric soliton-like humps well away from the interaction region of the KP web solution into a tail of multi-peaked oscillating profiles behind the main solitary hump. Computation indicates that the wave structure is modified near the center of the interaction region. Both analytical and numerical techniques are employed for working with non-periodic, non-decaying solutions on unbounded domains.

  20. On the evolution of perturbations to solutions of the Kadomtsev-Petviashvilli equation using the Benney-Luke equation

    Science.gov (United States)

    Ablowitz, Mark J.; Curtis, Christopher W.

    2011-05-01

    The Benney-Luke equation, which arises as a long wave asymptotic approximation of water waves, contains the Kadomtsev-Petviashvilli (KP) equation as a leading-order maximal balanced approximation. The question analyzed is how the Benney-Luke equation modifies the so-called web solutions of the KP equation. It is found that the Benney-Luke equation introduces dispersive radiation which breaks each of the symmetric soliton-like humps well away from the interaction region of the KP web solution into a tail of multi-peaked oscillating profiles behind the main solitary hump. Computation indicates that the wave structure is modified near the center of the interaction region. Both analytical and numerical techniques are employed for working with non-periodic, non-decaying solutions on unbounded domains.

  1. Study on monostable and bistable reaction-diffusion equations by iteration of travelling wave maps

    Science.gov (United States)

    Yi, Taishan; Chen, Yuming

    2017-12-01

    In this paper, based on the iterative properties of travelling wave maps, we develop a new method to obtain spreading speeds and asymptotic propagation for monostable and bistable reaction-diffusion equations. Precisely, for Dirichlet problems of monostable reaction-diffusion equations on the half line, by making links between travelling wave maps and integral operators associated with the Dirichlet diffusion kernel (the latter is NOT invariant under translation), we obtain some iteration properties of the Dirichlet diffusion and some a priori estimates on nontrivial solutions of Dirichlet problems under travelling wave transformation. We then provide the asymptotic behavior of nontrivial solutions in the space-time region for Dirichlet problems. These enable us to develop a unified method to obtain results on heterogeneous steady states, travelling waves, spreading speeds, and asymptotic spreading behavior for Dirichlet problem of monostable reaction-diffusion equations on R+ as well as of monostable/bistable reaction-diffusion equations on R.

  2. Terrestrial propagation of long electromagnetic waves

    CERN Document Server

    Galejs, Janis; Fock, V A

    2013-01-01

    Terrestrial Propagation of Long Electromagnetic Waves deals with the propagation of long electromagnetic waves confined principally to the shell between the earth and the ionosphere, known as the terrestrial waveguide. The discussion is limited to steady-state solutions in a waveguide that is uniform in the direction of propagation. Wave propagation is characterized almost exclusively by mode theory. The mathematics are developed only for sources at the ground surface or within the waveguide, including artificial sources as well as lightning discharges. This volume is comprised of nine chapte

  3. An Iterative Regularization Method for Identifying the Source Term in a Second Order Differential Equation

    Directory of Open Access Journals (Sweden)

    Fairouz Zouyed

    2015-01-01

    Full Text Available This paper discusses the inverse problem of determining an unknown source in a second order differential equation from measured final data. This problem is ill-posed; that is, the solution (if it exists does not depend continuously on the data. In order to solve the considered problem, an iterative method is proposed. Using this method a regularized solution is constructed and an a priori error estimate between the exact solution and its regularized approximation is obtained. Moreover, numerical results are presented to illustrate the accuracy and efficiency of this method.

  4. Travelling wave solutions for some time-delayed equations through factorizations

    International Nuclear Information System (INIS)

    Fahmy, E.S.

    2008-01-01

    In this work, we use factorization method to find explicit particular travelling wave solutions for the following important nonlinear second-order partial differential equations: The generalized time-delayed Burgers-Huxley, time-delayed convective Fishers, and the generalized time-delayed Burgers-Fisher. Using the particular solutions for these equations we find the general solutions, two-parameter solution, as special cases

  5. Wave equation dispersion inversion using a difference approximation to the dispersion-curve misfit gradient

    KAUST Repository

    Zhang, Zhendong

    2016-07-26

    We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh wave dispersion curve using a difference approximation to the gradient of the misfit function. We call this wave equation inversion of skeletonized surface waves because the skeletonized dispersion curve for the fundamental-mode Rayleigh wave is inverted using finite-difference solutions to the multi-dimensional elastic wave equation. The best match between the predicted and observed dispersion curves provides the optimal S-wave velocity model. Our method can invert for lateral velocity variations and also can mitigate the local minimum problem in full waveform inversion with a reasonable computation cost for simple models. Results with synthetic and field data illustrate the benefits and limitations of this method. © 2016 Elsevier B.V.

  6. A Laplace transform certified reduced basis method; application to the heat equation and wave equation

    OpenAIRE

    Knezevic, David; Patera, Anthony T.; Huynh, Dinh Bao Phuong

    2010-01-01

    We present a certified reduced basis (RB) method for the heat equation and wave equation. The critical ingredients are certified RB approximation of the Laplace transform; the inverse Laplace transform to develop the time-domain RB output approximation and rigorous error bound; a (Butterworth) filter in time to effect the necessary “modal” truncation; RB eigenfunction decomposition and contour integration for Offline–Online decomposition. We present numerical results to demonstrate the accura...

  7. Nonlinear dynamics of vortices in ultraclean type-II superconductors: Integrable wave equations in cylindrical geometry

    International Nuclear Information System (INIS)

    Coffey, M.W.

    1996-01-01

    Due to their short coherence lengths and relatively large energy gaps, the high-transition temperature superconductors are very likely candidates as ultraclean materials at low temperature. This class of materials features significantly modified vortex dynamics, with very little dissipation at low temperature. The motion is then dominated by wave propagation, being in general nonlinear. Here two-dimensional vortex motion is investigated in the ultraclean regime for a superconductor described in cylindrical geometry. The small-amplitude limit is assumed, and the focus is on the long-wavelength limit. Results for both zero and nonzero Hall force are presented, with the effects of nonlocal vortex interaction and vortex inertia being included within London theory. Linear and nonlinear problems are studied, with a predisposition toward the more analytically tractable situations. For a nonlinear problem in 2+1 dimensions, the cylindrical Kadomtsev-Petviashvili equation is derived. Hall angle measurements on high-T c superconductors indicate the need to investigate the properties of such a completely integrable wave equation. copyright 1996 The American Physical Society

  8. Solutions of deformed d'Alembert equation with quantum conformal symmetry

    International Nuclear Information System (INIS)

    Dobrev, V.K.; Kostadinov, B.S.

    1997-10-01

    We construct explicit solutions of a conditionally quantum conformal invariant q-d'Alembert equation proposed earlier by one of us. We give two types of solutions - polynomial solutions and a q-deformation of the plane wave. The latter is a formal power series in the noncommutative coordinates of q-Minkowski space-time and four-momenta. This q-plane wave has analogous properties to the classical one, in particular, it has the properties of q-Lorentz covariance, and it satisfies the q-d'Alembert equation on the q-Lorentz covariant momentum cone. On the other hand, our q-plane wave is not an exponent or q-exponent. Thus, it differs conceptually from the classical plane wave and may serve as a regularization. (author)

  9. The (′/-Expansion Method for Abundant Traveling Wave Solutions of Caudrey-Dodd-Gibbon Equation

    Directory of Open Access Journals (Sweden)

    Hasibun Naher

    2011-01-01

    Full Text Available We construct the traveling wave solutions of the fifth-order Caudrey-Dodd-Gibbon (CDG equation by the (/-expansion method. Abundant traveling wave solutions with arbitrary parameters are successfully obtained by this method and the wave solutions are expressed in terms of the hyperbolic, the trigonometric, and the rational functions. It is shown that the (/-expansion method is a powerful and concise mathematical tool for solving nonlinear partial differential equations.

  10. Differential field equations for the MHD waves and wave equation of Alfven; Las ecuaciones diferenciales de campo para las ondas MHD y la ecuacion de onda de Alfven

    Energy Technology Data Exchange (ETDEWEB)

    Fierros Palacios, Angel [Instituto de Investigaciones Electricas, Temixco, Morelos (Mexico)

    2001-02-01

    In this work the complete set of differential field equations which describes the dynamic state of a continuos conducting media which flow in presence of a perturbed magnetic field is obtained. Then, the thermic equation of state, the wave equation and the conservation law of energy for the Alfven MHD waves are obtained. [Spanish] Es este trabajo se obtiene el conjunto completo de ecuaciones diferenciales de campo que describen el estado dinamico de un medio continuo conductor que se mueve en presencia de un campo magnetico externo perturbado. Asi, se obtiene la ecuacion termica de estado, la ecuacion de onda y la ley de la conservacion de la energia para las ondas de Alfven de la MHD.

  11. Energy decay of a variable-coefficient wave equation with nonlinear time-dependent localized damping

    Directory of Open Access Journals (Sweden)

    Jieqiong Wu

    2015-09-01

    Full Text Available We study the energy decay for the Cauchy problem of the wave equation with nonlinear time-dependent and space-dependent damping. The damping is localized in a bounded domain and near infinity, and the principal part of the wave equation has a variable-coefficient. We apply the multiplier method for variable-coefficient equations, and obtain an energy decay that depends on the property of the coefficient of the damping term.

  12. Smooth and non-smooth traveling wave solutions of a class of nonlinear dispersive equation

    International Nuclear Information System (INIS)

    Zhao Xiaoshan; Wu Aidi; He Wenzhang

    2009-01-01

    There is the widespread existence of wave phenomena in physics, mechanics. This clearly necessitates a study of traveling waves in depth and of the modeling and analysis involved. In this paper, we study a nonlinear dispersive K(n,-n,2n) equation, which can be regarded as a generalized K(n,n) equation. Applying the bifurcation theory and the method of phase portraits analysis, we obtain the dynamical behavior and special exact solutions of the K(n,-n,2n) equation. As a result, the conditions under which peakon and compacton solutions appear are also given and the analytic expressions of peakon solutions, compacton and periodic cusp wave solutions are obtained.

  13. Two modified symplectic partitioned Runge-Kutta methods for solving the elastic wave equation

    Science.gov (United States)

    Su, Bo; Tuo, Xianguo; Xu, Ling

    2017-08-01

    Based on a modified strategy, two modified symplectic partitioned Runge-Kutta (PRK) methods are proposed for the temporal discretization of the elastic wave equation. The two symplectic schemes are similar in form but are different in nature. After the spatial discretization of the elastic wave equation, the ordinary Hamiltonian formulation for the elastic wave equation is presented. The PRK scheme is then applied for time integration. An additional term associated with spatial discretization is inserted into the different stages of the PRK scheme. Theoretical analyses are conducted to evaluate the numerical dispersion and stability of the two novel PRK methods. A finite difference method is used to approximate the spatial derivatives since the two schemes are independent of the spatial discretization technique used. The numerical solutions computed by the two new schemes are compared with those computed by a conventional symplectic PRK. The numerical results, which verify the new method, are superior to those generated by traditional conventional methods in seismic wave modeling.

  14. Traveling Wave Solutions of Reaction-Diffusion Equations Arising in Atherosclerosis Models

    Directory of Open Access Journals (Sweden)

    Narcisa Apreutesei

    2014-05-01

    Full Text Available In this short review article, two atherosclerosis models are presented, one as a scalar equation and the other one as a system of two equations. They are given in terms of reaction-diffusion equations in an infinite strip with nonlinear boundary conditions. The existence of traveling wave solutions is studied for these models. The monostable and bistable cases are introduced and analyzed.

  15. Scattering of lower-hybrid waves by drift-wave density fluctuations: solutions of the radiative transfer equation

    International Nuclear Information System (INIS)

    Andrews, P.L.; Perkins, F.W.

    1983-01-01

    The investigation of the scattering of lower-hybrid waves by density fluctuations arising from drift waves in tokamaks is distinguished by the presence in the wave equation of a large, random, derivative-coupling term. The propagation of the lower-hybrid waves is well represented by a radiative transfer equation when the scale size of the density fluctuations is small compared to the overall plasma size. The radiative transfer equation is solved in two limits: first, the forward scattering limit, where the scale size of density fluctuations is large compared to the lower-hybrid perpendicular wavelength, and second, the large-angle scattering limit, where this inequality is reversed. The most important features of these solutions are well represented by analytical formulas derived by simple arguments. Based on conventional estimates for density fluctuations arising from drift waves and a parabolic density profile, the optical depth tau for scattering through a significant angle, is given by tauroughly-equal(2/N 2 /sub parallel/) (#betta#/sub p/i0/#betta#) 2 (m/sub e/c 2 /2T/sub i/)/sup 1/2/ [c/α(Ω/sub i/Ω/sub e/)/sup 1/2/ ], where #betta#/sub p/i0 is the central ion plasma frequency and T/sub i/ denotes the ion temperature near the edge of the plasma. Most of the scattering occurs near the surface. The transmission through the scattering region scales as tau - 1 and the emerging intensity has an angular spectrum proportional to cos theta, where sin theta = k/sub perpendicular/xB/sub p//(k/sub perpendicular/B/sub p/), and B/sub p/ is the poloidal field

  16. Generalized intermediate long-wave hierarchy in zero-curvature representation with noncommutative spectral parameter

    Science.gov (United States)

    Degasperis, A.; Lebedev, D.; Olshanetsky, M.; Pakuliak, S.; Perelomov, A.; Santini, P. M.

    1992-11-01

    The simplest generalization of the intermediate long-wave hierarchy (ILW) is considered to show how to extend the Zakharov-Shabat dressing method to nonlocal, i.e., integro-partial differential, equations. The purpose is to give a procedure of constructing the zero-curvature representation of this class of equations. This result obtains by combining the Drinfeld-Sokolov formalism together with the introduction of an operator-valued spectral parameter, namely, a spectral parameter that does not commute with the space variable x. This extension provides a connection between the ILWk hierarchy and the Saveliev-Vershik continuum graded Lie algebras. In the case of ILW2 the Fairlie-Zachos sinh-algebra was found.

  17. Classification of homoclinic rogue wave solutions of the nonlinear Schrödinger equation

    Science.gov (United States)

    Osborne, A. R.

    2014-01-01

    Certain homoclinic solutions of the nonlinear Schrödinger (NLS) equation, with spatially periodic boundary conditions, are the most common unstable wave packets associated with the phenomenon of oceanic rogue waves. Indeed the homoclinic solutions due to Akhmediev, Peregrine and Kuznetsov-Ma are almost exclusively used in scientific and engineering applications. Herein I investigate an infinite number of other homoclinic solutions of NLS and show that they reduce to the above three classical homoclinic solutions for particular spectral values in the periodic inverse scattering transform. Furthermore, I discuss another infinity of solutions to the NLS equation that are not classifiable as homoclinic solutions. These latter are the genus-2N theta function solutions of the NLS equation: they are the most general unstable spectral solutions for periodic boundary conditions. I further describe how the homoclinic solutions of the NLS equation, for N = 1, can be derived directly from the theta functions in a particular limit. The solutions I address herein are actual spectral components in the nonlinear Fourier transform theory for the NLS equation: The periodic inverse scattering transform. The main purpose of this paper is to discuss a broader class of rogue wave packets1 for ship design, as defined in the Extreme Seas program. The spirit of this research came from D. Faulkner (2000) who many years ago suggested that ship design procedures, in order to take rogue waves into account, should progress beyond the use of simple sine waves. 1An overview of other work in the field of rogue waves is given elsewhere: Osborne 2010, 2012 and 2013. See the books by Olagnon and colleagues 2000, 2004 and 2008 for the Brest meetings. The books by Kharif et al. (2008) and Pelinovsky et al. (2010) are excellent references.

  18. Wave equation dispersion inversion using a difference approximation to the dispersion-curve misfit gradient

    KAUST Repository

    Zhang, Zhendong; Schuster, Gerard T.; Liu, Yike; Hanafy, Sherif M.; Li, Jing

    2016-01-01

    We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh wave dispersion curve using a difference approximation to the gradient of the misfit function. We call this wave equation inversion of skeletonized

  19. Regular behaviors in SU(2) Yang-Mills classical mechanics

    International Nuclear Information System (INIS)

    Xu Xiaoming

    1997-01-01

    In order to study regular behaviors in high-energy nucleon-nucleon collisions, a representation of the vector potential A i a is defined with respect to the (a,i)-dependence in the SU(2) Yang-Mills classical mechanics. Equations of the classical infrared field as well as effective potentials are derived for the elastic or inelastic collision of two plane wave in a three-mode model and the decay of an excited spherically-symmetric field

  20. Explicit Solutions and Bifurcations for a Class of Generalized Boussinesq Wave Equation

    International Nuclear Information System (INIS)

    Ma Zhi-Min; Sun Yu-Huai; Liu Fu-Sheng

    2013-01-01

    In this paper, the generalized Boussinesq wave equation u tt — u xx + a(u m ) xx + bu xxxx = 0 is investigated by using the bifurcation theory and the method of phase portraits analysis. Under the different parameter conditions, the exact explicit parametric representations for solitary wave solutions and periodic wave solutions are obtained. (general)

  1. Small data global solutions for the Camassa–Choi equations

    Science.gov (United States)

    Harrop-Griffiths, Benjamin; Marzuola, Jeremy L.

    2018-05-01

    We consider solutions to the Cauchy problem for an internal-wave model derived by Camassa–Choi (1996 J. Fluid Mech. 313 83–103). This model is a natural generalization of the Benjamin–Ono and intermediate long wave equations for weak transverse effects as in the case of the Kadomtsev–Petviashvili equations for the Korteweg-de Vries equation. For that reason they are often referred to as the KP-ILW or the KP–Benjamin–Ono equations regarding finite or infinite depth respectively. We prove the existence and long-time dynamics of global solutions from small, smooth, spatially localized initial data on . The techniques applied here involve testing by wave packet techniques developed by Ifrim and Tataru in (2015 Nonlinearity 28 2661–75 2016 Bull. Soc. Math. France 144 369–94).

  2. New compacton solutions and solitary wave solutions of fully nonlinear generalized Camassa-Holm equations

    International Nuclear Information System (INIS)

    Tian Lixin; Yin Jiuli

    2004-01-01

    In this paper, we introduce the fully nonlinear generalized Camassa-Holm equation C(m,n,p) and by using four direct ansatzs, we obtain abundant solutions: compactons (solutions with the absence of infinite wings), solitary patterns solutions having infinite slopes or cups, solitary waves and singular periodic wave solutions and obtain kink compacton solutions and nonsymmetry compacton solutions. We also study other forms of fully nonlinear generalized Camassa-Holm equation, and their compacton solutions are governed by linear equations

  3. The scalar wave equation in a Schwarzschild spacetime

    International Nuclear Information System (INIS)

    Stewart, J.M.; Schmidt, B.G.

    1978-09-01

    This paper studies the asymptotic behaviour of solutions of the zero rest mass scalar wave equation in the Schwarzschild spacetime in a neighbourhood of spatial infinity, which includes parts of future and past null infinity. The behaviour of such fields is essentially different from that which accurs in a flat spacetime. (orig.) [de

  4. Plane waves and spherical means applied to partial differential equations

    CERN Document Server

    John, Fritz

    2004-01-01

    Elementary and self-contained, this heterogeneous collection of results on partial differential equations employs certain elementary identities for plane and spherical integrals of an arbitrary function, showing how a variety of results on fairly general differential equations follow from those identities. The first chapter deals with the decomposition of arbitrary functions into functions of the type of plane waves. Succeeding chapters introduce the first application of the Radon transformation and examine the solution of the initial value problem for homogeneous hyperbolic equations with con

  5. Exponential decay for solutions to semilinear damped wave equation

    KAUST Repository

    Gerbi, Sté phane; Said-Houari, Belkacem

    2011-01-01

    This paper is concerned with decay estimate of solutions to the semilinear wave equation with strong damping in a bounded domain. Intro- ducing an appropriate Lyapunov function, we prove that when the damping is linear, we can find initial data

  6. On the regularity of mild solutions to complete higher order differential equations on Banach spaces

    Directory of Open Access Journals (Sweden)

    Nezam Iraniparast

    2015-09-01

    Full Text Available For the complete higher order differential equation u(n(t=Σk=0n-1Aku(k(t+f(t, t∈ R (* on a Banach space E, we give a new definition of mild solutions of (*. We then characterize the regular admissibility of a translation invariant subspace al M of BUC(R, E with respect to (* in terms of solvability of the operator equation Σj=0n-1AjXal Dj-Xal Dn = C. As application, almost periodicity of mild solutions of (* is proved.

  7. Stability properties of solitary waves for fractional KdV and BBM equations

    Science.gov (United States)

    Angulo Pava, Jaime

    2018-03-01

    This paper sheds new light on the stability properties of solitary wave solutions associated with Korteweg-de Vries-type models when the dispersion is very low. Using a compact, analytic approach and asymptotic perturbation theory, we establish sufficient conditions for the existence of exponentially growing solutions to the linearized problem and so a criterium of spectral instability of solitary waves is obtained for both models. Moreover, the nonlinear stability and spectral instability of the ground state solutions for both models is obtained for some specific regimen of parameters. Via a Lyapunov strategy and a variational analysis, we obtain the stability of the blow-up of solitary waves for the critical fractional KdV equation. The arguments presented in this investigation show promise for use in the study of the instability of traveling wave solutions of other nonlinear evolution equations.

  8. General characteristics of long waves around the South African Coast

    CSIR Research Space (South Africa)

    Rossouw, M

    2013-09-01

    Full Text Available Long-period waves are almost invisible waves due to the long wave-lengths of several hundreds of metres and heights of only decimetres. The effect of these long waves can, however, be devastating in the form of harbour basin oscillations...

  9. On the instability of wave-fields with JONSWAP spectra to inhomogeneous disturbances, and the consequent long-time evolution

    Science.gov (United States)

    Ribal, A.; Stiassnie, M.; Babanin, A.; Young, I.

    2012-04-01

    The instability of two-dimensional wave-fields and its subsequent evolution in time are studied by means of the Alber equation for narrow-banded random surface-waves in deep water subject to inhomogeneous disturbances. A linear partial differential equation (PDE) is obtained after applying an inhomogeneous disturbance to the Alber's equation and based on the solution of this PDE, the instability of the ocean wave surface is studied for a JONSWAP spectrum, which is a realistic ocean spectrum with variable directional spreading and steepness. The steepness of the JONSWAP spectrum depends on γ and α which are the peak-enhancement factor and energy scale of the spectrum respectively and it is found that instability depends on the directional spreading, α and γ. Specifically, if the instability stops due to the directional spreading, increase of the steepness by increasing α or γ can reactivate it. This result is in qualitative agreement with the recent large-scale experiment and new theoretical results. In the instability area of α-γ plane, a long-time evolution has been simulated by integrating Alber's equation numerically and recurrent evolution is obtained which is the stochastic counterpart of the Fermi-Pasta-Ulam recurrence obtained for the cubic Schrödinger equation.

  10. The damped wave equation with unbounded damping

    Czech Academy of Sciences Publication Activity Database

    Freitas, P.; Siegl, Petr; Tretter, C.

    2018-01-01

    Roč. 264, č. 12 (2018), s. 7023-7054 ISSN 0022-0396 Institutional support: RVO:61389005 Keywords : damped wave equation * unbounded damping * essential spectrum * quadratic operator funciton with unbounded coefficients * Schrodinger operators with complex potentials Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 1.988, year: 2016

  11. Statistical approach to LHCD modeling using the wave kinetic equation

    International Nuclear Information System (INIS)

    Kupfer, K.; Moreau, D.; Litaudon, X.

    1993-04-01

    Recent work has shown that for parameter regimes typical of many present day current drive experiments, the orbits of the launched LH rays are chaotic (in the Hamiltonian sense), so that wave energy diffuses through the stochastic layer and fills the spectral gap. We have analyzed this problem using a statistical approach, by solving the wave kinetic equation for the coarse-grained spectral energy density. An interesting result is that the LH absorption profile is essentially independent of both the total injected power and the level of wave stochastic diffusion

  12. The Multi-Wave Method for Exact Solutions of Nonlinear Partial Differential Equations

    Directory of Open Access Journals (Sweden)

    Yusuf Pandir

    2018-02-01

    Full Text Available In this research, we use the multi-wave method to obtain new exact solutions for generalized forms of 5th order KdV equation and fth order KdV (fKdV equation with power law nonlinearity. Computations are performed with the help of the mathematics software Mathematica. Then, periodic wave solutions, bright soliton solutions and rational function solutions with free parameters are obtained by this approach. It is shown that this method is very useful and effective.

  13. Travelling wave solutions to the K-P-P equation at supercritical wave speeds: a parallel to Simon Harris' probabilistic analysis

    NARCIS (Netherlands)

    Kyprianou, A.E.

    2000-01-01

    Recently Harris using probabilistic methods alone has given new proofs for the known existence asymptotics and unique ness of travelling wave solutions to the KPP equation Following in this vein we outline alternative probabilistic proofs for wave speeds exceeding the critical minimal wave speed

  14. Heat-flow equation motivated by the ideal-gas shock wave.

    Science.gov (United States)

    Holian, Brad Lee; Mareschal, Michel

    2010-08-01

    We present an equation for the heat-flux vector that goes beyond Fourier's Law of heat conduction, in order to model shockwave propagation in gases. Our approach is motivated by the observation of a disequilibrium among the three components of temperature, namely, the difference between the temperature component in the direction of a planar shock wave, versus those in the transverse directions. This difference is most prominent near the shock front. We test our heat-flow equation for the case of strong shock waves in the ideal gas, which has been studied in the past and compared to Navier-Stokes solutions. The new heat-flow treatment improves the agreement with nonequilibrium molecular-dynamics simulations of hard spheres under strong shockwave conditions.

  15. Electromagnetic interactions in relativistic infinite component wave equations

    International Nuclear Information System (INIS)

    Gerry, C.C.

    1979-01-01

    The electromagnetic interactions of a composite system described by relativistic infinite-component wave equations are considered. The noncompact group SO(4,2) is taken as the dynamical group of the systems, and its unitary irreducible representations, which are infinite dimensional, are used to find the energy spectra and to specify the states of the systems. First the interaction mechanism is examined in the nonrelativistic SO(4,2) formulation of the hydrogen atom as a heuristic guide. A way of making a minimal relativistic generalization of the minimal ineractions in the nonrelativistic equation for the hydrogen atom is proposed. In order to calculate the effects of the relativistic minimal interactions, a covariant perturbation theory suitable for infinite-component wave equations, which is an algebraic and relativistic version of the Rayleigh-Schroedinger perturbation theory, is developed. The electric and magnetic polarizabilities for the ground state of the hydrogen atom are calculated. The results have the correct nonrelativistic limits. Next, the relativistic cross section of photon absorption by the atom is evaluated. A relativistic expression for the cross section of light scattering corresponding to the seagull diagram is derived. The Born amplitude is combusted and the role of spacelike solutions is discussed. Finally, internal electromagnetic interactions that give rise to the fine structure splittings, the Lamb shifts and the hyperfine splittings are considered. The spin effects are introduced by extending the dynamical group

  16. Relating systems properties of the wave and the Schrödinger equation

    NARCIS (Netherlands)

    Zwart, Heiko J.; Le Gorrec, Yann; Maschke, B.M.

    In this article we show that systems properties of the systems governed by the second order differential equation d2wdt2=−A0w and the first order differential equation dzdt=iA0z are related. This can be used to show that, for instance, exact observability of the N-dimensional wave equation implies

  17. A single-sided representation for the homogeneous Green's function of a unified scalar wave equation.

    Science.gov (United States)

    Wapenaar, Kees

    2017-06-01

    A unified scalar wave equation is formulated, which covers three-dimensional (3D) acoustic waves, 2D horizontally-polarised shear waves, 2D transverse-electric EM waves, 2D transverse-magnetic EM waves, 3D quantum-mechanical waves and 2D flexural waves. The homogeneous Green's function of this wave equation is a combination of the causal Green's function and its time-reversal, such that their singularities at the source position cancel each other. A classical representation expresses this homogeneous Green's function as a closed boundary integral. This representation finds applications in holographic imaging, time-reversed wave propagation and Green's function retrieval by cross correlation. The main drawback of the classical representation in those applications is that it requires access to a closed boundary around the medium of interest, whereas in many practical situations the medium can be accessed from one side only. Therefore, a single-sided representation is derived for the homogeneous Green's function of the unified scalar wave equation. Like the classical representation, this single-sided representation fully accounts for multiple scattering. The single-sided representation has the same applications as the classical representation, but unlike the classical representation it is applicable in situations where the medium of interest is accessible from one side only.

  18. New exact travelling wave solutions for two potential coupled KdV equations with symbolic computation

    International Nuclear Information System (INIS)

    Yang Zonghang

    2007-01-01

    We find new exact travelling wave solutions for two potential KdV equations which are presented by Foursov [Foursov MV. J Math Phys 2000;41:6173-85]. Compared with the extended tanh-function method, the algorithm used in our paper can obtain some new kinds of exact travelling wave solutions. With the aid of symbolic computation, some novel exact travelling wave solutions of the potential KdV equations are constructed

  19. Quadratic PBW-Algebras, Yang-Baxter Equation and Artin-Schelter Regularity

    International Nuclear Information System (INIS)

    Gateva-Ivanova, Tatiana

    2010-08-01

    We study quadratic algebras over a field k. We show that an n-generated PBW-algebra A has finite global dimension and polynomial growth iff its Hilbert series is H A (z) = 1/(1-z) n . A surprising amount can be said when the algebra A has quantum binomial relations, that is the defining relations are binomials xy - c xy zt, c xy is an element of k x , which are square-free and nondegenerate. We prove that in this case various good algebraic and homological properties are closely related. The main result shows that for an n-generated quantum binomial algebra A the following conditions are equivalent: (i) A is a PBW-algebra with finite global dimension; (ii) A is PBW and has polynomial growth; (iii) A is an Artin-Schelter regular PBW-algebra; (iv) A is a Yang-Baxter algebra; (v) H A (z) = 1/(1-z) n ; (vi) The dual A ! is a quantum Grassman algebra; (vii) A is a binomial skew polynomial ring. This implies that the problem of classification of Artin-Schelter regular PBW-algebras of global dimension n is equivalent to the classification of square-free set-theoretic solutions of the Yang-Baxter equation (X,r), on sets X of order n.| (author)

  20. The two-wave X-ray field calculated by means of integral-equation methods

    International Nuclear Information System (INIS)

    Bremer, J.

    1984-01-01

    The problem of calculating the two-wave X-ray field on the basis of the Takagi-Taupin equations is discussed for the general case of curved lattice planes. A two-dimensional integral equation which incorporates the nature of the incoming radiation, the form of the crystal/vacuum boundary, and the curvature of the structure, is deduced. Analytical solutions for the symmetrical Laue case with incoming plane waves are obtained directly for perfect crystals by means of iteration. The same method permits a simple derivation of the narrow-wave Laue and Bragg cases. Modulated wave fronts are discussed, and it is shown that a cut-off in the width of an incoming plane wave leads to lateral oscillations which are superimposed on the Pendelloesung fringes. Bragg and Laue shadow fields are obtained. The influence of a non-zero kernel is discussed and a numerical procedure for calculating wave amplitudes in curved crystals is presented. (Auth.)

  1. Nonlinear wave equation in frequency domain: accurate modeling of ultrafast interaction in anisotropic nonlinear media

    DEFF Research Database (Denmark)

    Guo, Hairun; Zeng, Xianglong; Zhou, Binbin

    2013-01-01

    We interpret the purely spectral forward Maxwell equation with up to third-order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named the nonlinear wave equation in the frequency domain, includes quadratic and cubic...... nonlinearities, delayed Raman effects, and anisotropic nonlinearities. The full potential of this wave equation is demonstrated by investigating simulations of solitons generated in the process of ultrafast cascaded second-harmonic generation. We show that a balance in the soliton delay can be achieved due...

  2. Long-Range Piping Inspection by Ultrasonic Guided Waves

    International Nuclear Information System (INIS)

    Joo, Young Sang; Lim, Sa Hoe; Eom, Heung Seop; Kim, Jae Hee

    2005-01-01

    The ultrasonic guided waves are very promising for the long-range inspection of large structures because they can propagate a long distance along the structures such as plates, shells and pipes. The guided wave inspection could be utilized for an on-line monitoring technique when the transmitting and receiving transducers are positioned at a remote point on the structure. The received signal has the information about the integrity of the monitoring area between the transmitting and receiving transducers. On-line monitoring of a pipe line using an ultrasonic guided wave can detect flaws such as corrosion, erosion and fatigue cracking at an early stage and collect useful information on the flaws. However the guided wave inspection is complicated by the dispersive characteristics for guided waves. The phase and group velocities are a function of the frequency-thickness product. Therefore, the different frequency components of the guided waves will travel at different speeds and the shape of the received signal will changed as it propagates along the pipe. In this study, we analyze the propagation characteristics of guided wave modes in a small diameter pipe of nuclear power plant and select the suitable mode for a long-range inspection. And experiments will be carried out for the practical application of a long-range inspection in a 26m long pipe by using a high-power ultrasonic inspection system

  3. Reduction of the Breit Coulomb equation to an equivalent Schroedinger equation, and investigation of the behavior of the wave function near the origin

    International Nuclear Information System (INIS)

    Malenfant, J.

    1988-01-01

    The Breit equation for two equal-mass spin-1/2 particles interacting through an attractive Coulomb potential is separated into its angular and radial parts, obtaining coupled sets of first-order differential equations for the radial wave functions. The radial equations for the 1 J/sub J/, 3 J/sub J/, and 3 P 0 states are further reduced to a single, one-dimensional Schroedinger equation with a relatively simple effective potential. No approximations, other than the initial one of an instantaneous Coulomb interaction, are made in deriving this equation; it accounts for all relativistic effects, as well as for mixing between different components of the wave function. Approximate solutions are derived for this Schroedinger equation, which gives the correct O(α 4 ) term for the 1 1 S 0 energy and for the n 1 J/sub J/ energies, for J>0. The radial equations for the 3 (J +- 1)/sub J/ states are reduced to two second-order coupled equations. At small r, the Breit Coulomb wave functions behave as r/sup ν//sup -1/, where ν is either √J(J+1)+1-α 2 /4 or √J(J+1)-α 2 /4 . The 1 S 0 and 3 P 0 wave functions therefore diverge at the origin as r/sup //sup √//sup 1-//sup α//sup <2//4 -1$. This divergence of the J = 0 states, however, does not occur when the spin-spin interaction, -(α/r)αxα, is added to the Coulomb potential

  4. Asymptotic Behavior of Periodic Wave Solution to the Hirota—Satsuma Equation

    International Nuclear Information System (INIS)

    Wu Yong-Qi

    2011-01-01

    The one- and two-periodic wave solutions for the Hirota—Satsuma (HS) equation are presented by using the Hirota derivative and Riemann theta function. The rigorous proofs on asymptotic behaviors of these two solutions are given such that soliton solution can be obtained from the periodic wave solution in an appropriate limiting procedure. (general)

  5. The wave equation on a curved space-time

    International Nuclear Information System (INIS)

    Friedlander, F.G.

    1975-01-01

    It is stated that chapters on differential geometry, distribution theory, and characteristics and the propagation of discontinuities are preparatory. The main matter is in three chapters, entitled: fundamental solutions, representation theorems, and wave equations on n-dimensional space-times. These deal with general construction of fundamental solutions and their application to the Cauchy problem. (U.K.)

  6. Semilinear damped wave equation in locally uniform spaces

    Czech Academy of Sciences Publication Activity Database

    Michálek, Martin; Pražák, D.; Slavík, J.

    2017-01-01

    Roč. 16, č. 5 (2017), s. 1673-1695 ISSN 1534-0392 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : damped wave equations * nonlinear damping * unbounded domains Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.801, year: 2016 http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=14110

  7. On the so called rogue waves in nonlinear Schrodinger equations

    Directory of Open Access Journals (Sweden)

    Y. Charles Li

    2016-04-01

    Full Text Available The mechanism of a rogue water wave is still unknown. One popular conjecture is that the Peregrine wave solution of the nonlinear Schrodinger equation (NLS provides a mechanism. A Peregrine wave solution can be obtained by taking the infinite spatial period limit to the homoclinic solutions. In this article, from the perspective of the phase space structure of these homoclinic orbits in the infinite dimensional phase space where the NLS defines a dynamical system, we examine the observability of these homoclinic orbits (and their approximations. Our conclusion is that these approximate homoclinic orbits are the most observable solutions, and they should correspond to the most common deep ocean waves rather than the rare rogue waves. We also discuss other possibilities for the mechanism of a rogue wave: rough dependence on initial data or finite time blow up.

  8. Angle-domain Migration Velocity Analysis using Wave-equation Reflection Traveltime Inversion

    KAUST Repository

    Zhang, Sanzong

    2012-11-04

    The main difficulty with an iterative waveform inversion is that it tends to get stuck in a local minima associated with the waveform misfit function. This is because the waveform misfit function is highly non-linear with respect to changes in the velocity model. To reduce this nonlinearity, we present a reflection traveltime tomography method based on the wave equation which enjoys a more quasi-linear relationship between the model and the data. A local crosscorrelation of the windowed downgoing direct wave and the upgoing reflection wave at the image point yields the lag time that maximizes the correlation. This lag time represents the reflection traveltime residual that is back-projected into the earth model to update the velocity in the same way as wave-equation transmission traveltime inversion. The residual movemout analysis in the angle-domain common image gathers provides a robust estimate of the depth residual which is converted to the reflection traveltime residual for the velocity inversion. We present numerical examples to demonstrate its efficiency in inverting seismic data for complex velocity model.

  9. Wave equation of a nonlinear triatomic molecule and the adiabatic correction to the Born--Oppenheimer approximation

    International Nuclear Information System (INIS)

    Bardo, R.D.; Wolfsberg, M.

    1977-01-01

    The wave equation for a nonlinear polyatomic molecule is formulated in molecule-fixed coordinates by a method originally due to Hirschfelder and Wigner. Application is made to a triatomic molecule, and the wave equation is explicitly presented in a useful molecule-fixed coordinate system. The formula for the adiabatic correction to the Born--Oppenheimer approximation for a triatomic molecule is obtained. The extension of the present formulation to larger polyatomic molecules is pointed out. Some terms in the triatomic molecule wave equation are discussed in detail

  10. Runge-Kutta Integration of the Equal Width Wave Equation Using the Method of Lines

    Directory of Open Access Journals (Sweden)

    M. A. Banaja

    2015-01-01

    Full Text Available The equal width (EW equation governs nonlinear wave phenomena like waves in shallow water. Numerical solution of the (EW equation is obtained by using the method of lines (MOL based on Runge-Kutta integration. Using von Neumann stability analysis, the scheme is found to be unconditionally stable. Solitary wave motion and interaction of two solitary waves are studied using the proposed method. The three invariants of the motion are evaluated to determine the conservation properties of the generated scheme. Accuracy of the proposed method is discussed by computing the L2 and L∞ error norms. The results are found in good agreement with exact solution.

  11. NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION.

    Science.gov (United States)

    Liu, F; Meerschaert, M M; McGough, R J; Zhuang, P; Liu, Q

    2013-03-01

    In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

  12. An inhomogeneous wave equation and non-linear Diophantine approximation

    DEFF Research Database (Denmark)

    Beresnevich, V.; Dodson, M. M.; Kristensen, S.

    2008-01-01

    A non-linear Diophantine condition involving perfect squares and arising from an inhomogeneous wave equation on the torus guarantees the existence of a smooth solution. The exceptional set associated with the failure of the Diophantine condition and hence of the existence of a smooth solution...

  13. Global Regularity and Time Decay for the 2D Magnetohydrodynamic Equations with Fractional Dissipation and Partial Magnetic Diffusion

    Science.gov (United States)

    Dong, Bo-Qing; Jia, Yan; Li, Jingna; Wu, Jiahong

    2018-05-01

    This paper focuses on a system of the 2D magnetohydrodynamic (MHD) equations with the kinematic dissipation given by the fractional operator (-Δ )^α and the magnetic diffusion by partial Laplacian. We are able to show that this system with any α >0 always possesses a unique global smooth solution when the initial data is sufficiently smooth. In addition, we make a detailed study on the large-time behavior of these smooth solutions and obtain optimal large-time decay rates. Since the magnetic diffusion is only partial here, some classical tools such as the maximal regularity property for the 2D heat operator can no longer be applied. A key observation on the structure of the MHD equations allows us to get around the difficulties due to the lack of full Laplacian magnetic diffusion. The results presented here are the sharpest on the global regularity problem for the 2D MHD equations with only partial magnetic diffusion.

  14. The existence and regularity of time-periodic solutions to the three-dimensional Navier–Stokes equations in the whole space

    International Nuclear Information System (INIS)

    Kyed, Mads

    2014-01-01

    The existence, uniqueness and regularity of time-periodic solutions to the Navier–Stokes equations in the three-dimensional whole space are investigated. We consider the Navier–Stokes equations with a non-zero drift term corresponding to the physical model of a fluid flow around a body that moves with a non-zero constant velocity. The existence of a strong time-periodic solution is shown for small time-periodic data. It is further shown that this solution is unique in a large class of weak solutions that can be considered physically reasonable. Finally, we establish regularity properties for any strong solution regardless of its size. (paper)

  15. Local-in-space blow-up criteria for a class of nonlinear dispersive wave equations

    Science.gov (United States)

    Novruzov, Emil

    2017-11-01

    This paper is concerned with blow-up phenomena for the nonlinear dispersive wave equation on the real line, ut -uxxt +[ f (u) ] x -[ f (u) ] xxx +[ g (u) + f″/(u) 2 ux2 ] x = 0 that includes the Camassa-Holm equation as well as the hyperelastic-rod wave equation (f (u) = ku2 / 2 and g (u) = (3 - k) u2 / 2) as special cases. We establish some a local-in-space blow-up criterion (i.e., a criterion involving only the properties of the data u0 in a neighborhood of a single point) simplifying and precising earlier blow-up criteria for this equation.

  16. The two-fermion relativistic wave equations of Constraint Theory in the Pauli-Schroedinger form

    International Nuclear Information System (INIS)

    Mourad, J.; Sazdjian, H.

    1994-01-01

    The two-fermion relativistic wave equations of Constraint Theory are reduced, after expressing the components of the 4x4 matrix wave function in terms of one of the 2x2 components, to a single equation of the Pauli-Schroedinger type, valid for all sectors of quantum numbers. The potentials that are present belong to the general classes of scalar, pseudoscalar and vector interactions and are calculable in perturbation theory from Feynman diagrams. In the limit when one of the masses becomes infinite, the equation reduces to the two-component form of the one-particle Dirac equation with external static potentials. The Hamiltonian, to order 1/c 2 , reproduces most of the known theoretical results obtained by other methods. The gauge invariance of the wave equation is checked, to that order, in the case of QED. The role of the c.m. energy dependence of the relativistic interquark confining potential is emphasized and the structure of the Hamiltonian, to order 1/c 2 , corresponding to confining scalar potentials, is displayed. (authors). 32 refs., 2 figs

  17. Travelling Waves in Hyperbolic Chemotaxis Equations

    KAUST Repository

    Xue, Chuan; Hwang, Hyung Ju; Painter, Kevin J.; Erban, Radek

    2010-01-01

    Mathematical models of bacterial populations are often written as systems of partial differential equations for the densities of bacteria and concentrations of extracellular (signal) chemicals. This approach has been employed since the seminal work of Keller and Segel in the 1970s (Keller and Segel, J. Theor. Biol. 30:235-248, 1971). The system has been shown to permit travelling wave solutions which correspond to travelling band formation in bacterial colonies, yet only under specific criteria, such as a singularity in the chemotactic sensitivity function as the signal approaches zero. Such a singularity generates infinite macroscopic velocities which are biologically unrealistic. In this paper, we formulate a model that takes into consideration relevant details of the intracellular processes while avoiding the singularity in the chemotactic sensitivity. We prove the global existence of solutions and then show the existence of travelling wave solutions both numerically and analytically. © 2010 Society for Mathematical Biology.

  18. Travelling Waves in Hyperbolic Chemotaxis Equations

    KAUST Repository

    Xue, Chuan

    2010-10-16

    Mathematical models of bacterial populations are often written as systems of partial differential equations for the densities of bacteria and concentrations of extracellular (signal) chemicals. This approach has been employed since the seminal work of Keller and Segel in the 1970s (Keller and Segel, J. Theor. Biol. 30:235-248, 1971). The system has been shown to permit travelling wave solutions which correspond to travelling band formation in bacterial colonies, yet only under specific criteria, such as a singularity in the chemotactic sensitivity function as the signal approaches zero. Such a singularity generates infinite macroscopic velocities which are biologically unrealistic. In this paper, we formulate a model that takes into consideration relevant details of the intracellular processes while avoiding the singularity in the chemotactic sensitivity. We prove the global existence of solutions and then show the existence of travelling wave solutions both numerically and analytically. © 2010 Society for Mathematical Biology.

  19. Higher-order rogue wave solutions of the three-wave resonant interaction equation via the generalized Darboux transformation

    International Nuclear Information System (INIS)

    Wang, Xin; Chen, Yong; Cao, Jianli

    2015-01-01

    In this paper, we utilize generalized Darboux transformation to study higher-order rogue wave solutions of the three-wave resonant interaction equation, which describes the propagation and mixing of waves with different frequencies in weakly nonlinear dispersive media. A general Nth-order rogue wave solution with two characteristic velocities structural parameters and 3N independent parameters under a determined plane-wave background and a specific parameter condition is derived. As an application, we show that four fundamental rogue waves with fundamental, two kinds of line and quadrilateral patterns, or six fundamental rogue waves with fundamental, triangular, two kinds of quadrilateral and circular patterns can emerge in the second-order rogue waves. Moreover, several important wave characteristics including the maximum values, the corresponding coordinate positions of the humps, and the stability problem for some special higher-order rogue wave solutions such as the fundamental and quadrilateral cases are discussed. (paper)

  20. Ince's limits for confluent and double-confluent Heun equations

    International Nuclear Information System (INIS)

    Figueiredo, B.D. Bonorino

    2005-01-01

    We find pairs of solutions to a differential equation which is obtained as a special limit of a generalized spheroidal wave equation (this is also known as confluent Heun equation). One solution in each pair is given by a series of hypergeometric functions and converges for any finite value of the independent variable z, while the other is given by a series of modified Bessel functions and converges for vertical bar z vertical bar > vertical bar z 0 vertical bar, where z 0 denotes a regular singularity. For short, the preceding limit is called Ince's limit after Ince who have used the same procedure to get the Mathieu equations from the Whittaker-Hill ones. We find as well that, when z 0 tends to zero, the Ince limit of the generalized spheroidal wave equation turns out to be the Ince limit of a double-confluent Heun equation, for which solutions are provided. Finally, we show that the Schroedinger equation for inverse fourth- and sixth-power potentials reduces to peculiar cases of the double-confluent Heun equation and its Ince's limit, respectively

  1. Solving the KPI wave equation with a moving adaptive FEM grid

    Directory of Open Access Journals (Sweden)

    Granville Sewell

    2013-04-01

    Full Text Available The Kadomtsev-Petviashvili I (KPI equation is the difficult nonlinear wave equation $U_{xt} + 6U_x^2 + 6UU_{xx} + U_{xxxx} = 3U_{yy}.$ We solve this equation using PDE2D (www.pde2d.com with initial conditions consisting of two lump solitons, which collide and reseparate. Since the solution has steep, moving, peaks, an adaptive finite element grid is used with a grading which moves with the peaks.

  2. Full-Wave Ambient Noise Tomography of the Long Valley Volcanic Region (California)

    Science.gov (United States)

    Flinders, A. F.; Shelly, D. R.; Dawson, P. B.; Hill, D. P.; Shen, Y.

    2017-12-01

    In the late 1970s, and throughout the 1990s, Long Valley Caldera (California) experienced intense periods of unrest characterized by uplift of the resurgent dome, earthquake swarms, and CO2 emissions around Mammoth Mountain. While modeling of the uplift and gravity changes support the possibility of new magmatic intrusions beneath the caldera, geologic interpretations conclude that the magmatic system underlying the caldera is moribund. Geophysical studies yield diverse versions of a sizable but poorly resolved low-velocity zone at depth (> 6km), yet whether this zone is indicative of a significant volume of crystal mush, smaller isolated pockets of partial melt, or magmatic fluids, is inconclusive. The nature of this low-velocity zone, and the state of volcano's magmatic system, carry important implications for the significance of resurgent-dome inflation and the nature of associated hazards. To better characterize this low-velocity zone we present preliminary results from a 3D full-waveform ambient-noise seismic tomography model derived from the past 25 years of vertical component broadband and short-period seismic data. This new study uses fully numerical solutions of the wave equation to account for the complex wave propagation in a heterogeneous, 3D earth model, including wave interaction with topography. The method ensures that wave propagation is modeled accurately in 3D, enabling the full use of seismic records. By using empirical Green's functions, derived from ambient noise and modeled as Rayleigh surface waves, we are able to extend model resolution to depths beyond the limits of previous local earthquake studies. The model encompasses not only the Long Valley Caldera, but the entire Long Valley Volcanic Region, including Mammoth Mountain and the Mono Crater/Inyo Domes volcanic chain.

  3. Regularization of fields for self-force problems in curved spacetime: Foundations and a time-domain application

    International Nuclear Information System (INIS)

    Vega, Ian; Detweiler, Steven

    2008-01-01

    We propose an approach for the calculation of self-forces, energy fluxes and waveforms arising from moving point charges in curved spacetimes. As opposed to mode-sum schemes that regularize the self-force derived from the singular retarded field, this approach regularizes the retarded field itself. The singular part of the retarded field is first analytically identified and removed, yielding a finite, differentiable remainder from which the self-force is easily calculated. This regular remainder solves a wave equation which enjoys the benefit of having a nonsingular source. Solving this wave equation for the remainder completely avoids the calculation of the singular retarded field along with the attendant difficulties associated with numerically modeling a delta-function source. From this differentiable remainder one may compute the self-force, the energy flux, and also a waveform which reflects the effects of the self-force. As a test of principle, we implement this method using a 4th-order (1+1) code, and calculate the self-force for the simple case of a scalar charge moving in a circular orbit around a Schwarzschild black hole. We achieve agreement with frequency-domain results to ∼0.1% or better.

  4. Mixed Total Variation and L1 Regularization Method for Optical Tomography Based on Radiative Transfer Equation

    Directory of Open Access Journals (Sweden)

    Jinping Tang

    2017-01-01

    Full Text Available Optical tomography is an emerging and important molecular imaging modality. The aim of optical tomography is to reconstruct optical properties of human tissues. In this paper, we focus on reconstructing the absorption coefficient based on the radiative transfer equation (RTE. It is an ill-posed parameter identification problem. Regularization methods have been broadly applied to reconstruct the optical coefficients, such as the total variation (TV regularization and the L1 regularization. In order to better reconstruct the piecewise constant and sparse coefficient distributions, TV and L1 norms are combined as the regularization. The forward problem is discretized with the discontinuous Galerkin method on the spatial space and the finite element method on the angular space. The minimization problem is solved by a Jacobian-based Levenberg-Marquardt type method which is equipped with a split Bregman algorithms for the L1 regularization. We use the adjoint method to compute the Jacobian matrix which dramatically improves the computation efficiency. By comparing with the other imaging reconstruction methods based on TV and L1 regularizations, the simulation results show the validity and efficiency of the proposed method.

  5. Dark and composite rogue waves in the coupled Hirota equations

    International Nuclear Information System (INIS)

    Chen, Shihua

    2014-01-01

    The intriguing dark and composite rogue wave dynamics in a coupled Hirota system are unveiled, based on the exact explicit rational solutions obtained under the assumption of equal background height. It is found that a dark rogue wave state would occur as a result of the strong coupling between two field components with large wavenumber difference, and there would appear plenty of composite structures that are attributed to the specific wavenumber difference and the free choice of three independent structural parameters. The coexistence of different fundamental rogue waves in such a coupled system is also demonstrated. - Highlights: • Exact rational rogue wave solutions under different parameter conditions are presented for the coupled Hirota equations. • The basic rogue wave features and hence the intriguing dark structures are unveiled. • We attributed the diversity of composite rogue wave dynamics to the free choice of three independent structural parameters. • The remarkable coexisting rogue wave behaviors in such a coupled system are demonstrated

  6. Sound Propagation Around Off-Shore Wind Turbines. Long-Range Parabolic Equation Calculations for Baltic Sea Conditions

    Energy Technology Data Exchange (ETDEWEB)

    Johansson, Lisa

    2003-07-01

    Low-frequency, long-range sound propagation over a sea surface has been calculated using a wide-angel Cranck-Nicholson Parabolic Equation method. The model is developed to investigate noise from off-shore wind turbines. The calculations are made using normal meteorological conditions of the Baltic Sea. Special consideration has been made to a wind phenomenon called low level jet with strong winds on rather low altitude. The effects of water waves on sound propagation have been incorporated in the ground boundary condition using a boss model. This way of including roughness in sound propagation models is valid for water wave heights that are small compared to the wave length of the sound. Nevertheless, since only low frequency sound is considered, waves up to the mean wave height of the Baltic Sea can be included in this manner. The calculation model has been tested against benchmark cases and agrees well with measurements. The calculations show that channelling of sound occurs at downwind conditions and that the sound propagation tends towards cylindrical spreading. The effects of the water waves are found to be fairly small.

  7. Diffusive Wave Approximation to the Shallow Water Equations: Computational Approach

    KAUST Repository

    Collier, Nathan; Radwan, Hany; Dalcin, Lisandro; Calo, Victor M.

    2011-01-01

    We discuss the use of time adaptivity applied to the one dimensional diffusive wave approximation to the shallow water equations. A simple and computationally economical error estimator is discussed which enables time-step size adaptivity

  8. Travelling wave solutions and proper solutions to the two-dimensional Burgers-Korteweg-de Vries equation

    International Nuclear Information System (INIS)

    Feng Zhaosheng

    2003-01-01

    In this paper, we study the two-dimensional Burgers-Korteweg-de Vries (2D-BKdV) equation by analysing an equivalent two-dimensional autonomous system, which indicates that under some particular conditions, the 2D-BKdV equation has a unique bounded travelling wave solution. Then by using a direct method, a travelling solitary wave solution to the 2D-BKdV equation is expressed explicitly, which appears to be more efficient than the existing methods proposed in the literature. At the end of the paper, the asymptotic behaviour of the proper solutions of the 2D-BKdV equation is established by applying the qualitative theory of differential equations

  9. Test of a new heat-flow equation for dense-fluid shock waves.

    Science.gov (United States)

    Holian, Brad Lee; Mareschal, Michel; Ravelo, Ramon

    2010-09-21

    Using a recently proposed equation for the heat-flux vector that goes beyond Fourier's Law of heat conduction, we model shockwave propagation in the dense Lennard-Jones fluid. Disequilibrium among the three components of temperature, namely, the difference between the kinetic temperature in the direction of a planar shock wave and those in the transverse directions, particularly in the region near the shock front, gives rise to a new transport (equilibration) mechanism not seen in usual one-dimensional heat-flow situations. The modification of the heat-flow equation was tested earlier for the case of strong shock waves in the ideal gas, which had been studied in the past and compared to Navier-Stokes-Fourier solutions. Now, the Lennard-Jones fluid, whose equation of state and transport properties have been determined from independent calculations, allows us to study the case where potential, as well as kinetic contributions are important. The new heat-flow treatment improves the agreement with nonequilibrium molecular-dynamics simulations under strong shock wave conditions, compared to Navier-Stokes.

  10. Scattering of quantized solitary waves in the cubic Schrodinger equation

    International Nuclear Information System (INIS)

    Dolan, L.

    1976-01-01

    The quantum mechanics for N particles interacting via a delta-function potential in one space dimension and one time dimension is known. The second-quantized description of this system has for its Euler-Lagrange equations of motion the cubic Schrodinger equation. This nonlinear differential equation supports solitary wave solutions. A quantization of these solitons reproduces the weak-coupling limit to the known quantum mechanics. The phase shift for two-body scattering and the energy of the N-body bound state is derived in this approximation. The nonlinear Schrodinger equation is contrasted with the sine-Gordon theory in respect to the ideas which the classical solutions play in the description of the quantum states

  11. Four-dimensional integral equations for the MHD diffraction waves in plasma

    International Nuclear Information System (INIS)

    Alexandrova, A.A.; Khizhnyak, N.A.

    2000-01-01

    The superficial analysis of the boundary-value nonstationary problem for Alfven wave has shown the principal possibility of using the method of evolutionary integral equations of non-stationary macroscopic electrodynamical in a case of MHD description of waves in plasma. With the importance of strict mathematical solutions obtained for simple model problems that is the diffraction of one separately taken Alfven wave is that it can be the basis for construction of the approximate solutions of more complex boundary-value problems

  12. Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes

    DEFF Research Database (Denmark)

    Zhang, H.W.; Schäffer, Hemming Andreas

    2007-01-01

    An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoe unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done...... by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application....

  13. Three-Dimensional Coupled NLS Equations for Envelope Gravity Solitary Waves in Baroclinic Atmosphere and Modulational Instability

    Directory of Open Access Journals (Sweden)

    Baojun Zhao

    2018-01-01

    Full Text Available Envelope gravity solitary waves are an important research hot spot in the field of solitary wave. And the weakly nonlinear model equations system is a part of the research of envelope gravity solitary waves. Because of the lack of technology and theory, previous studies tried hard to reduce the variable numbers and constructed the two-dimensional model in barotropic atmosphere and could only describe the propagation feature in a direction. But for the propagation of envelope gravity solitary waves in real ocean ridges and atmospheric mountains, the three-dimensional model is more appropriate. Meanwhile, the baroclinic problem of atmosphere is also an inevitable topic. In the paper, the three-dimensional coupled nonlinear Schrödinger (CNLS equations are presented to describe the evolution of envelope gravity solitary waves in baroclinic atmosphere, which are derived from the basic dynamic equations by employing perturbation and multiscale methods. The model overcomes two disadvantages: (1 baroclinic problem and (2 propagation path problem. Then, based on trial function method, we deduce the solution of the CNLS equations. Finally, modulational instability of wave trains is also discussed.

  14. Application of perturbation theory to a P-wave eikonal equation in orthorhombic media

    KAUST Repository

    Stovas, Alexey; Masmoudi, Nabil; Alkhalifah, Tariq Ali

    2016-01-01

    The P-wave eikonal equation for orthorhombic (ORT) anisotropic media is a highly nonlinear partial differential equation requiring the solution of a sixth-order polynomial to obtain traveltimes, resulting in complex and time-consuming numerical

  15. Traveling waves and the renormalization group improvedBalitsky-Kovchegov equation

    Energy Technology Data Exchange (ETDEWEB)

    Enberg, Rikard

    2006-12-01

    I study the incorporation of renormalization group (RG)improved BFKL kernels in the Balitsky-Kovchegov (BK) equation whichdescribes parton saturation. The RG improvement takes into accountimportant parts of the next-to-leading and higher order logarithmiccorrections to the kernel. The traveling wave front method for analyzingthe BK equation is generalized to deal with RG-resummed kernels,restricting to the interesting case of fixed QCD coupling. The resultsshow that the higher order corrections suppress the rapid increase of thesaturation scale with increasing rapidity. I also perform a "diffusive"differential equation approximation, which illustrates that someimportant qualitative properties of the kernel change when including RGcorrections.

  16. Nonlinear waves in plasma with negative ion

    International Nuclear Information System (INIS)

    Saito, Maki; Watanabe, Shinsuke; Tanaca, Hiroshi.

    1984-01-01

    The propagation of nonlinear ion wave is investigated theoretically in a plasma with electron, positive ion and negative ion. The ion wave of long wavelength is described by a modified K-dV equation instead of a K-dV equation when the nonlinear coefficient of the K-dV equation vanishes at the critical density of negative ion. In the vicinity of the critical density, the ion wave is described by a coupled K-dV and modified K-dV equation. The transition from a compressional soliton to a rarefactive soliton and vice versa are examined by the coupled equation as a function of the negative ion density. The ion wave of short wavelength is described by a nonlinear Schroedinger equation. In the plasma with a negative ion, the nonlinear coefficient of the nonlinear Schroedinger equation changes the sign and the ion wave becomes modulationally unstable. (author)

  17. Nonlinear integrodifferential equations as discrete systems

    Science.gov (United States)

    Tamizhmani, K. M.; Satsuma, J.; Grammaticos, B.; Ramani, A.

    1999-06-01

    We analyse a class of integrodifferential equations of the `intermediate long wave' (ILW) type. We show that these equations can be formally interpreted as discrete, differential-difference systems. This allows us to link equations of this type with previous results of ours involving differential-delay equations and, on the basis of this, propose new integrable equations of ILW type. Finally, we extend this approach to pure difference equations and propose ILW forms for the discrete lattice KdV equation.

  18. Inverse random source scattering for the Helmholtz equation in inhomogeneous media

    Science.gov (United States)

    Li, Ming; Chen, Chuchu; Li, Peijun

    2018-01-01

    This paper is concerned with an inverse random source scattering problem in an inhomogeneous background medium. The wave propagation is modeled by the stochastic Helmholtz equation with the source driven by additive white noise. The goal is to reconstruct the statistical properties of the random source such as the mean and variance from the boundary measurement of the radiated random wave field at multiple frequencies. Both the direct and inverse problems are considered. We show that the direct problem has a unique mild solution by a constructive proof. For the inverse problem, we derive Fredholm integral equations, which connect the boundary measurement of the radiated wave field with the unknown source function. A regularized block Kaczmarz method is developed to solve the ill-posed integral equations. Numerical experiments are included to demonstrate the effectiveness of the proposed method.

  19. Long-wave equivalent viscoelastic solids for porous rocks saturated by two-phase fluids

    Science.gov (United States)

    Santos, J. E.; Savioli, G. B.

    2018-04-01

    Seismic waves traveling across fluid-saturated poroelastic materials with mesoscopic-scale heterogeneities induce fluid flow and Biot's slow waves generating energy loss and velocity dispersion. Using Biot's equations of motion to model these type of heterogeneities would require extremely fine meshes. We propose a numerical upscaling procedure to determine the complex and frequency dependent P-wave and shear moduli of an effective viscoelastic medium long-wave equivalent to a poroelastic solid saturated by a two-phase fluid. The two-phase fluid is defined in terms of capillary pressure and relative permeability flow functions. The P-wave and shear effective moduli are determined using harmonic compressibility and shear experiments applied on representative samples of the bulk material. Each experiment is associated with a boundary value problem that is solved using the finite element method. Since a poroelastic solid saturated by a two-phase fluid supports the existence of two slow waves, this upscaling procedure allows to analyze their effect on the mesoscopic-loss mechanism in hydrocarbon reservoir formations. Numerical results show that a two-phase Biot medium model predicts higher attenuation than classic Biot models.

  20. Shock formation in small-data solutions to 3D quasilinear wave equations

    CERN Document Server

    Speck, Jared

    2016-01-01

    In 1848 James Challis showed that smooth solutions to the compressible Euler equations can become multivalued, thus signifying the onset of a shock singularity. Today it is known that, for many hyperbolic systems, such singularities often develop. However, most shock-formation results have been proved only in one spatial dimension. Serge Alinhac's groundbreaking work on wave equations in the late 1990s was the first to treat more than one spatial dimension. In 2007, for the compressible Euler equations in vorticity-free regions, Demetrios Christodoulou remarkably sharpened Alinhac's results and gave a complete description of shock formation. In this monograph, Christodoulou's framework is extended to two classes of wave equations in three spatial dimensions. It is shown that if the nonlinear terms fail to satisfy the null condition, then for small data, shocks are the only possible singularities that can develop. Moreover, the author exhibits an open set of small data whose solutions form a shock, and he prov...

  1. On Landweber–Kaczmarz methods for regularizing systems of ill-posed equations in Banach spaces

    International Nuclear Information System (INIS)

    Leitão, A; Alves, M Marques

    2012-01-01

    In this paper, iterative regularization methods of Landweber–Kaczmarz type are considered for solving systems of ill-posed equations modeled (finitely many) by operators acting between Banach spaces. Using assumptions of uniform convexity and smoothness on the parameter space, we are able to prove a monotony result for the proposed method, as well as to establish convergence (for exact data) and stability results (in the noisy data case). (paper)

  2. New multidimensional partially integrable generalization of S-integrable N-wave equation

    International Nuclear Information System (INIS)

    Zenchuk, A. I.

    2007-01-01

    This paper develops a modification of the dressing method based on the inhomogeneous linear integral equation with integral operator having nonempty kernel. The method allows one to construct the systems of multidimensional partial differential equations having differential polynomial structure in any dimension n. The associated solution space is not full, although it is parametrized by certain number of arbitrary functions of (n-1) variables. We consider four-dimensional generalization of the classical (2+1)-dimensional S-integrable N-wave equation as an example

  3. Traveling Wave Solutions of ZK-BBM Equation Sine-Cosine Method

    Directory of Open Access Journals (Sweden)

    Sadaf Bibi

    2014-03-01

    Full Text Available Travelling wave solutions are obtained by using a relatively new technique which is called sine-cosine method for ZK-BBM equations. Solution procedure and obtained results re-confirm the efficiency of the proposed scheme.

  4. EXACT SOLITARY WAVE SOLUTIONS TO A CLASS OF NONLINEAR DIFFERENTIAL EQUATIONS USING DIRECT ALGEBRAIC METHOD

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    Using direct algebraic method,exact solitary wave solutions are performed for a class of third order nonlinear dispersive disipative partial differential equations. These solutions are obtained under certain conditions for the relationship between the coefficients of the equation. The exact solitary waves of this class are rational functions of real exponentials of kink-type solutions.

  5. On the global "two-sided" characteristic Cauchy problem for linear wave equations on manifolds

    Science.gov (United States)

    Lupo, Umberto

    2018-04-01

    The global characteristic Cauchy problem for linear wave equations on globally hyperbolic Lorentzian manifolds is examined, for a class of smooth initial value hypersurfaces satisfying favourable global properties. First it is shown that, if geometrically well-motivated restrictions are placed on the supports of the (smooth) initial datum and of the (smooth) inhomogeneous term, then there exists a continuous global solution which is smooth "on each side" of the initial value hypersurface. A uniqueness result in Sobolev regularity H^{1/2+ɛ }_{loc} is proved among solutions supported in the union of the causal past and future of the initial value hypersurface, and whose product with the indicator function of the causal future (resp. past) of the hypersurface is past compact (resp. future compact). An explicit representation formula for solutions is obtained, which prominently features an invariantly defined, densitised version of the null expansion of the hypersurface. Finally, applications to quantum field theory on curved spacetimes are briefly discussed.

  6. A well-conditioned integral-equation formulation for efficient transient analysis of electrically small microelectronic devices

    KAUST Repository

    Bagci, Hakan

    2010-05-01

    A hierarchically regularized coupled set of time-domain surface and volume electric field integral-equations (TD-S-EFIE and TD-V-EFIE) for analyzing electromagnetic wave interactions with electrically small and geometrically intricate composite structures comprising perfect electrically conducting surfaces and finite dielectric volumes is presented. A classically formulated coupled set of TD-S- and V-EFIEs is shown to be ill-conditioned at low frequencies owing to the hypersingular nature of the TD-S-EFIE. To eliminate low-frequency breakdown in marching-on-in-time solvers for these coupled equations, a hierarchical regularizer leveraging generalized RaoWiltonGlisson functions is applied to the TD-S-EFIE; no regularization is applied to the TD-V-EFIE as it is protected from low-frequency breakdown by an identity term. The resulting hierarchically regularized hybrid TD-S- and V-EFIE solver is applicable to the analysis of wave interactions with electrically small and densely meshed structures of arbitrary topology. The accuracy, efficiency, and applicability of the proposed solver are demonstrated by analyzing crosstalk in a six-port transmission line, radiation from a miniature radio-frequency identification antenna, and, plane-wave coupling onto a partially-shielded and fully loaded two-layer computer board. © 2006 IEEE.

  7. Robust Imaging Methodology for Challenging Environments: Wave Equation Dispersion Inversion of Surface Waves

    KAUST Repository

    Li, Jing

    2017-12-22

    A robust imaging technology is reviewed that provide subsurface information in challenging environments: wave-equation dispersion inversion (WD) of surface waves for the shear velocity model. We demonstrate the benefits and liabilities of the method with synthetic seismograms and field data. The benefits of WD are that 1) there is no layered medium assumption, as there is in conventional inversion of dispersion curves, so that the 2D or 3D S-velocity model can be reliably obtained with seismic surveys over rugged topography, and 2) WD mostly avoids getting stuck in local minima. The synthetic and field data examples demonstrate that WD can accurately reconstruct the S-wave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic media and the inversion of dispersion curves associated with Love wave. The liability is that is almost as expensive as FWI and only recovers the Vs distribution to a depth no deeper than about 1/2~1/3 wavelength.

  8. Numerical response analysis of a large mat-type floating structure in regular waves; Matogata choogata futai kozobutsu no haro oto kaiseki

    Energy Technology Data Exchange (ETDEWEB)

    Yasuzawa, Y.; Kagawa, K.; Kitabayashi, K. [Kyushu University, Fukuoka (Japan); Kawano, D. [Mitsubishi Heavy Industries, Ltd., Tokyo (Japan)

    1997-08-01

    The theory and formulation for the numerical response analysis of a large floating structure in regular waves were given. This paper also reports the comparison between the experiment in the Shipping Research Institute in the Minitry of Transport and the result calculated using numerical analytic codes in this study. The effect of the bending rigidity of a floating structure and the wave direction on the dynamic response of a structure was examined by numerical calculation. When the ratio of structure length and incident wavelength (L/{lambda}) is lower, the response amplitude on the transmission side becomes higher in a wave-based response. The hydrodynamic elasticity exerts a dominant influence when L/{lambda} becomes higher. For incident oblique waves, the maximum response does not necessarily appear on the incidence side. Moreover, the response distribution is also complicated. For example, the portion where any flexible amplitude hardly appears exists. A long structure response can be predicted from a short structure response to some degree. They differ in response properties when the ridigity based on the similarity rule largely differs, irrespective of the same L/{lambda}. For higher L/{lambda}, the wave response can be easily predicted when the diffrection force is replaced by the concentrated exciting force on the incidence side. 13 refs., 14 figs., 3 tabs.

  9. Dimensional regularization and renormalization of Coulomb gauge quantum electrodynamics

    International Nuclear Information System (INIS)

    Heckathorn, D.

    1979-01-01

    Quantum electrodynamics is renormalized in the Coulomb gauge with covariant counter terms and without momentum-dependent wave-function renormalization constants. It is shown how to dimensionally regularize non-covariant integrals occurring in this guage, and prove that the 'minimal' subtraction prescription excludes non-covariant counter terms. Motivated by the need for a renormalized Coulomb gauge formalism in certain practical calculations, the author introduces a convenient prescription with physical parameters. The renormalization group equations for the Coulomb gauge are derived. (Auth.)

  10. An efficient hybrid pseudospectral/finite-difference scheme for solving the TTI pure P-wave equation

    KAUST Repository

    Zhan, Ge

    2013-02-19

    The pure P-wave equation for modelling and migration in tilted transversely isotropic (TTI) media has attracted more and more attention in imaging seismic data with anisotropy. The desirable feature is that it is absolutely free of shear-wave artefacts and the consequent alleviation of numerical instabilities generally suffered by some systems of coupled equations. However, due to several forward-backward Fourier transforms in wavefield updating at each time step, the computational cost is significant, and thereby hampers its prevalence. We propose to use a hybrid pseudospectral (PS) and finite-difference (FD) scheme to solve the pure P-wave equation. In the hybrid solution, most of the cost-consuming wavenumber terms in the equation are replaced by inexpensive FD operators, which in turn accelerates the computation and reduces the computational cost. To demonstrate the benefit in cost saving of the new scheme, 2D and 3D reverse-time migration (RTM) examples using the hybrid solution to the pure P-wave equation are carried out, and respective runtimes are listed and compared. Numerical results show that the hybrid strategy demands less computation time and is faster than using the PS method alone. Furthermore, this new TTI RTM algorithm with the hybrid method is computationally less expensive than that with the FD solution to conventional TTI coupled equations. © 2013 Sinopec Geophysical Research Institute.

  11. An efficient hybrid pseudospectral/finite-difference scheme for solving the TTI pure P-wave equation

    International Nuclear Information System (INIS)

    Zhan, Ge; Pestana, Reynam C; Stoffa, Paul L

    2013-01-01

    The pure P-wave equation for modelling and migration in tilted transversely isotropic (TTI) media has attracted more and more attention in imaging seismic data with anisotropy. The desirable feature is that it is absolutely free of shear-wave artefacts and the consequent alleviation of numerical instabilities generally suffered by some systems of coupled equations. However, due to several forward–backward Fourier transforms in wavefield updating at each time step, the computational cost is significant, and thereby hampers its prevalence. We propose to use a hybrid pseudospectral (PS) and finite-difference (FD) scheme to solve the pure P-wave equation. In the hybrid solution, most of the cost-consuming wavenumber terms in the equation are replaced by inexpensive FD operators, which in turn accelerates the computation and reduces the computational cost. To demonstrate the benefit in cost saving of the new scheme, 2D and 3D reverse-time migration (RTM) examples using the hybrid solution to the pure P-wave equation are carried out, and respective runtimes are listed and compared. Numerical results show that the hybrid strategy demands less computation time and is faster than using the PS method alone. Furthermore, this new TTI RTM algorithm with the hybrid method is computationally less expensive than that with the FD solution to conventional TTI coupled equations. (paper)

  12. Hyperbolic partial differential equations populations, reactors, tides and waves theory and applications

    CERN Document Server

    Witten, Matthew

    1983-01-01

    Hyperbolic Partial Differential Equations, Volume 1: Population, Reactors, Tides and Waves: Theory and Applications covers three general areas of hyperbolic partial differential equation applications. These areas include problems related to the McKendrick/Von Foerster population equations, other hyperbolic form equations, and the numerical solution.This text is composed of 15 chapters and begins with surveys of age specific population interactions, populations models of diffusion, nonlinear age dependent population growth with harvesting, local and global stability for the nonlinear renewal eq

  13. Gaussian solitary waves for the logarithmic-KdV and the logarithmic-KP equations

    International Nuclear Information System (INIS)

    Wazwaz, Abdul-Majid

    2014-01-01

    We investigate the logarithmic-KdV equation for more Gaussian solitary waves. We extend this work to derive the logarithmic-KP (Kadomtsev–Petviashvili) equation. We show that both logarithmic models are characterized by their Gaussian solitons. (paper)

  14. The Role of the Pressure in the Partial Regularity Theory for Weak Solutions of the Navier-Stokes Equations

    Science.gov (United States)

    Chamorro, Diego; Lemarié-Rieusset, Pierre-Gilles; Mayoufi, Kawther

    2018-04-01

    We study the role of the pressure in the partial regularity theory for weak solutions of the Navier-Stokes equations. By introducing the notion of dissipative solutions, due to D uchon and R obert (Nonlinearity 13:249-255, 2000), we will provide a generalization of the Caffarelli, Kohn and Nirenberg theory. Our approach sheels new light on the role of the pressure in this theory in connection to Serrin's local regularity criterion.

  15. Extended common-image-point gathers for anisotropic wave-equation migration

    KAUST Repository

    Sava, Paul C.; Alkhalifah, Tariq Ali

    2010-01-01

    In regions characterized by complex subsurface structure, wave-equation depth migration is a powerful tool for accurately imaging the earth’s interior. The quality of the final image greatly depends on the quality of the model which includes

  16. A fast-multipole domain decomposition integral equation solver for characterizing electromagnetic wave propagation in mine environments

    KAUST Repository

    Yücel, Abdulkadir C.

    2013-07-01

    Reliable and effective wireless communication and tracking systems in mine environments are key to ensure miners\\' productivity and safety during routine operations and catastrophic events. The design of such systems greatly benefits from simulation tools capable of analyzing electromagnetic (EM) wave propagation in long mine tunnels and large mine galleries. Existing simulation tools for analyzing EM wave propagation in such environments employ modal decompositions (Emslie et. al., IEEE Trans. Antennas Propag., 23, 192-205, 1975), ray-tracing techniques (Zhang, IEEE Tran. Vehic. Tech., 5, 1308-1314, 2003), and full wave methods. Modal approaches and ray-tracing techniques cannot accurately account for the presence of miners and their equipments, as well as wall roughness (especially when the latter is comparable to the wavelength). Full-wave methods do not suffer from such restrictions but require prohibitively large computational resources. To partially alleviate this computational burden, a 2D integral equation-based domain decomposition technique has recently been proposed (Bakir et. al., in Proc. IEEE Int. Symp. APS, 1-2, 8-14 July 2012). © 2013 IEEE.

  17. Consistent three-equation model for thin films

    Science.gov (United States)

    Richard, Gael; Gisclon, Marguerite; Ruyer-Quil, Christian; Vila, Jean-Paul

    2017-11-01

    Numerical simulations of thin films of newtonian fluids down an inclined plane use reduced models for computational cost reasons. These models are usually derived by averaging over the fluid depth the physical equations of fluid mechanics with an asymptotic method in the long-wave limit. Two-equation models are based on the mass conservation equation and either on the momentum balance equation or on the work-energy theorem. We show that there is no two-equation model that is both consistent and theoretically coherent and that a third variable and a three-equation model are required to solve all theoretical contradictions. The linear and nonlinear properties of two and three-equation models are tested on various practical problems. We present a new consistent three-equation model with a simple mathematical structure which allows an easy and reliable numerical resolution. The numerical calculations agree fairly well with experimental measurements or with direct numerical resolutions for neutral stability curves, speed of kinematic waves and of solitary waves and depth profiles of wavy films. The model can also predict the flow reversal at the first capillary trough ahead of the main wave hump.

  18. Kondratiev cycles and so-called long waves. The early research

    NARCIS (Netherlands)

    J. Tinbergen (Jan)

    1981-01-01

    textabstractThis paper recalls some early work of the Dutch pioneers of long-wave research which anticipated many of the contemporary debates. Various explanations which have been advanced for the existence of long waves are reviewed, and the applicability of long-wave theories in a number of

  19. Attenuation compensation in least-squares reverse time migration using the visco-acoustic wave equation

    KAUST Repository

    Dutta, Gaurav

    2013-08-20

    Attenuation leads to distortion of amplitude and phase of seismic waves propagating inside the earth. Conventional acoustic and least-squares reverse time migration do not account for this distortion which leads to defocusing of migration images in highly attenuative geological environments. To account for this distortion, we propose to use the visco-acoustic wave equation for least-squares reverse time migration. Numerical tests on synthetic data show that least-squares reverse time migration with the visco-acoustic wave equation corrects for this distortion and produces images with better balanced amplitudes compared to the conventional approach. © 2013 SEG.

  20. Solution of the nonrelativistic wave equation using the tridiagonal representation approach

    Science.gov (United States)

    Alhaidari, A. D.

    2017-07-01

    We choose a complete set of square integrable functions as a basis for the expansion of the wavefunction in configuration space such that the matrix representation of the nonrelativistic time-independent linear wave operator is tridiagonal and symmetric. Consequently, the matrix wave equation becomes a symmetric three-term recursion relation for the expansion coefficients of the wavefunction. The recursion relation is then solved exactly in terms of orthogonal polynomials in the energy. Some of these polynomials are not found in the mathematics literature. The asymptotics of these polynomials give the phase shift for the continuous energy scattering states and the spectrum for the discrete energy bound states. Depending on the space and boundary conditions, the basis functions are written in terms of either the Laguerre or Jacobi polynomials. The tridiagonal requirement limits the number of potential functions that yield exact solutions of the wave equation. Nonetheless, the class of exactly solvable problems in this approach is larger than the conventional class (see, for example, Table XII in the text). We also give very accurate results for cases where the wave operator matrix is not tridiagonal but its elements could be evaluated either exactly or numerically with high precision.

  1. A constrained regularization method for inverting data represented by linear algebraic or integral equations

    Science.gov (United States)

    Provencher, Stephen W.

    1982-09-01

    CONTIN is a portable Fortran IV package for inverting noisy linear operator equations. These problems occur in the analysis of data from a wide variety experiments. They are generally ill-posed problems, which means that errors in an unregularized inversion are unbounded. Instead, CONTIN seeks the optimal solution by incorporating parsimony and any statistical prior knowledge into the regularizor and absolute prior knowledge into equallity and inequality constraints. This can be greatly increase the resolution and accuracyh of the solution. CONTIN is very flexible, consisting of a core of about 50 subprograms plus 13 small "USER" subprograms, which the user can easily modify to specify special-purpose constraints, regularizors, operator equations, simulations, statistical weighting, etc. Specjial collections of USER subprograms are available for photon correlation spectroscopy, multicomponent spectra, and Fourier-Bessel, Fourier and Laplace transforms. Numerically stable algorithms are used throughout CONTIN. A fairly precise definition of information content in terms of degrees of freedom is given. The regularization parameter can be automatically chosen on the basis of an F-test and confidence region. The interpretation of the latter and of error estimates based on the covariance matrix of the constrained regularized solution are discussed. The strategies, methods and options in CONTIN are outlined. The program itself is described in the following paper.

  2. Scalar evolution equations for shear waves in incompressible solids: a simple derivation of the Z, ZK, KZK and KP equations

    OpenAIRE

    Destrade, Michel; Goriely, Alain; Saccomandi, Giuseppe

    2011-01-01

    We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent, and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy-Green strain). However, we show that the Z equation c...

  3. Scattering of lower-hybrid waves by density fluctuations

    International Nuclear Information System (INIS)

    Andrews, P.L.; Perkins, F.W.

    1981-07-01

    The investigation of the scattering of lower-hybrid waves by density fluctuations in tokamaks is distinguished by the presence in the wave equation of a large, random, derivative-coupling term. Assuming the fluctuations to be of long wavelength compared to the incident wave the similarity of the wave equation to the Schroedinger equation for a particle in a random magnetic field is used to derive a two-way diffusion equation for the wave energy density. The diffusion constant found disagrees with earlier findings and the source of the discrepancy is pointed out. When the correct boundary conditions are imposed this equation can be solved by separation of variables. However most of the important features of the solution are apparent without detailed algebra

  4. Relativistic transport equation for a discontinuity wave of multiplicity one

    Energy Technology Data Exchange (ETDEWEB)

    Giambo, S; Palumbo, A [Istituto di Matematica, Universita degli Studi, Messina (Italy)

    1980-04-14

    In the framework of the theory of the singular hypersurfaces, the transport equation for the amplitude of a discontinuity wave, corresponding to a simple characteristic of a quasi-linear hyperbolic system, is established in the context of special relativity.

  5. Explicit and exact nontraveling wave solutions of the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation

    Science.gov (United States)

    Yuan, Na

    2018-04-01

    With the aid of the symbolic computation, we present an improved ( G ‧ / G ) -expansion method, which can be applied to seek more types of exact solutions for certain nonlinear evolution equations. In illustration, we choose the (3 + 1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation to demonstrate the validity and advantages of the method. As a result, abundant explicit and exact nontraveling wave solutions are obtained including two solitary waves solutions, nontraveling wave solutions and dromion soliton solutions. Some particular localized excitations and the interactions between two solitary waves are researched. The method can be also applied to other nonlinear partial differential equations.

  6. Introductory Applications of Partial Differential Equations With Emphasis on Wave Propagation and Diffusion

    CERN Document Server

    Lamb, George L

    1995-01-01

    INTRODUCTORY APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS. With Emphasis on Wave Propagation and Diffusion. This is the ideal text for students and professionals who have some familiarity with partial differential equations, and who now wish to consolidate and expand their knowledge. Unlike most other texts on this topic, it interweaves prior knowledge of mathematics and physics, especially heat conduction and wave motion, into a presentation that demonstrates their interdependence. The result is a superb teaching text that reinforces the reader's understanding of both mathematics and physic

  7. Ginzburg-Landau equations for a d-wave superconductor with applications to vortex structure and surface problems

    International Nuclear Information System (INIS)

    Xu, J.; Ren, Y.; Ting, C.S.

    1995-01-01

    The properties of a d x 2 -y 2 -wave superconductor in an external magnetic field are investigated on the basis of Gorkov's theory of weakly coupled superconductors. The Ginzburg-Landau (GL) equations, which govern the spatial variations of the order parameter and the supercurrent, are microscopically derived. The single vortex structure and surface problems in such a superconductor are studied using these equations. It is shown that the d-wave vortex structure is very different from the conventional s-wave vortex: the s-wave and d-wave components, with the opposite winding numbers, are found to coexist in the region near the vortex core. The supercurrent and local magnetic field around the vortex are calculated. Far away from the vortex core, both of them exhibit a fourfold symmetry, in contrast to an s-wave superconductor. The surface problem in a d-wave superconductor is also studied by solving the GL equations. The total order parameter near the surface is always a real combination of s- and d-wave components, which means that the proximity effect cannot induce a time-reversal symmetry-breaking state at the surface

  8. Statistics for long irregular wave run-up on a plane beach from direct numerical simulations

    Science.gov (United States)

    Didenkulova, Ira; Senichev, Dmitry; Dutykh, Denys

    2017-04-01

    Very often for global and transoceanic events, due to the initial wave transformation, refraction, diffraction and multiple reflections from coastal topography and underwater bathymetry, the tsunami approaches the beach as a very long wave train, which can be considered as an irregular wave field. The prediction of possible flooding and properties of the water flow on the coast in this case should be done statistically taking into account the formation of extreme (rogue) tsunami wave on a beach. When it comes to tsunami run-up on a beach, the most used mathematical model is the nonlinear shallow water model. For a beach of constant slope, the nonlinear shallow water equations have rigorous analytical solution, which substantially simplifies the mathematical formulation. In (Didenkulova et al. 2011) we used this solution to study statistical characteristics of the vertical displacement of the moving shoreline and its horizontal velocity. The influence of the wave nonlinearity was approached by considering modifications of probability distribution of the moving shoreline and its horizontal velocity for waves of different amplitudes. It was shown that wave nonlinearity did not affect the probability distribution of the velocity of the moving shoreline, while the vertical displacement of the moving shoreline was affected substantially demonstrating the longer duration of coastal floods with an increase in the wave nonlinearity. However, this analysis did not take into account the actual transformation of irregular wave field offshore to oscillations of the moving shoreline on a slopping beach. In this study we would like to cover this gap by means of extensive numerical simulations. The modeling is performed in the framework of nonlinear shallow water equations, which are solved using a modern shock-capturing finite volume method. Although the shallow water model does not pursue the wave breaking and bore formation in a general sense (including the water surface

  9. Qualitative analysis and traveling wave solutions for the perturbed nonlinear Schroedinger's equation with Kerr law nonlinearity

    International Nuclear Information System (INIS)

    Zhang Zaiyun; Liu Zhenhai; Miao Xiujin; Chen Yuezhong

    2011-01-01

    In this Letter, we investigate the perturbed nonlinear Schroedinger's equation (NLSE) with Kerr law nonlinearity. All explicit expressions of the bounded traveling wave solutions for the equation are obtained by using the bifurcation method and qualitative theory of dynamical systems. These solutions contain bell-shaped solitary wave solutions, kink-shaped solitary wave solutions and Jacobi elliptic function periodic solutions. Moreover, we point out the region which these periodic wave solutions lie in. We present the relation between the bounded traveling wave solution and the energy level h. We find that these periodic wave solutions tend to the corresponding solitary wave solutions as h increases or decreases. Finally, for some special selections of the energy level h, it is shown that the exact periodic solutions evolute into solitary wave solution.

  10. New Exact Travelling Wave and Periodic Solutions of Discrete Nonlinear Schroedinger Equation

    International Nuclear Information System (INIS)

    Yang Qin; Dai Chaoqing; Zhang Jiefang

    2005-01-01

    Some new exact travelling wave and period solutions of discrete nonlinear Schroedinger equation are found by using a hyperbolic tangent function approach, which was usually presented to find exact travelling wave solutions of certain nonlinear partial differential models. Now we can further extend the new algorithm to other nonlinear differential-different models.

  11. Asymptotic behaviors of solutions for viscoelastic wave equation with space-time dependent damping term

    KAUST Repository

    Said-Houari, Belkacem

    2012-03-01

    In this paper, we consider a viscoelastic wave equation with an absorbing term and space-time dependent damping term. Based on the weighted energy method, and by assuming that the kernel decaying exponentially, we obtain the L2 decay rates of the solutions. More precisely, we show that the decay rates are the same as those obtained in Lin et al. (2010) [15] for the semilinear wave equation with absorption term. © 2011 Elsevier Inc.

  12. Asymptotic behaviors of solutions for viscoelastic wave equation with space-time dependent damping term

    KAUST Repository

    Said-Houari, Belkacem

    2012-01-01

    In this paper, we consider a viscoelastic wave equation with an absorbing term and space-time dependent damping term. Based on the weighted energy method, and by assuming that the kernel decaying exponentially, we obtain the L2 decay rates of the solutions. More precisely, we show that the decay rates are the same as those obtained in Lin et al. (2010) [15] for the semilinear wave equation with absorption term. © 2011 Elsevier Inc.

  13. Viscoacoustic wave-equation traveltime inversion with correct and incorrect attenuation profiles

    KAUST Repository

    Yu, Han

    2017-08-17

    A visco-acoustic wave-equation traveltime inversion method is presented that inverts for a shallow subsurface velocity distribution with correct and incorrect attenuation profiles. Similar to the classical wave equation traveltime inversion, this method applies the misfit functional that minimizes the first break differences between the observed and predicted data. Although, WT can partly avoid the cycle skipping problem, an initial velocity model approaches to the right or wrong velocity models under different setups of the attenuation profiles. However, with a Q model far away from the real model, the inverted tomogram is obviously different from the true velocity model while a small change of the Q model does not improve the inversion quality in a strong manner if low frequency information is not lost.

  14. An Operator Method for Field Moments from the Extended Parabolic Wave Equation and Analytical Solutions of the First and Second Moments for Atmospheric Electromagnetic Wave Propagation

    Science.gov (United States)

    Manning, Robert M.

    2004-01-01

    The extended wide-angle parabolic wave equation applied to electromagnetic wave propagation in random media is considered. A general operator equation is derived which gives the statistical moments of an electric field of a propagating wave. This expression is used to obtain the first and second order moments of the wave field and solutions are found that transcend those which incorporate the full paraxial approximation at the outset. Although these equations can be applied to any propagation scenario that satisfies the conditions of application of the extended parabolic wave equation, the example of propagation through atmospheric turbulence is used. It is shown that in the case of atmospheric wave propagation and under the Markov approximation (i.e., the delta-correlation of the fluctuations in the direction of propagation), the usual parabolic equation in the paraxial approximation is accurate even at millimeter wavelengths. The comprehensive operator solution also allows one to obtain expressions for the longitudinal (generalized) second order moment. This is also considered and the solution for the atmospheric case is obtained and discussed. The methodology developed here can be applied to any qualifying situation involving random propagation through turbid or plasma environments that can be represented by a spectral density of permittivity fluctuations.

  15. A stochastic collocation method for the second order wave equation with a discontinuous random speed

    KAUST Repository

    Motamed, Mohammad

    2012-08-31

    In this paper we propose and analyze a stochastic collocation method for solving the second order wave equation with a random wave speed and subjected to deterministic boundary and initial conditions. The speed is piecewise smooth in the physical space and depends on a finite number of random variables. The numerical scheme consists of a finite difference or finite element method in the physical space and a collocation in the zeros of suitable tensor product orthogonal polynomials (Gauss points) in the probability space. This approach leads to the solution of uncoupled deterministic problems as in the Monte Carlo method. We consider both full and sparse tensor product spaces of orthogonal polynomials. We provide a rigorous convergence analysis and demonstrate different types of convergence of the probability error with respect to the number of collocation points for full and sparse tensor product spaces and under some regularity assumptions on the data. In particular, we show that, unlike in elliptic and parabolic problems, the solution to hyperbolic problems is not in general analytic with respect to the random variables. Therefore, the rate of convergence may only be algebraic. An exponential/fast rate of convergence is still possible for some quantities of interest and for the wave solution with particular types of data. We present numerical examples, which confirm the analysis and show that the collocation method is a valid alternative to the more traditional Monte Carlo method for this class of problems. © 2012 Springer-Verlag.

  16. Transition from regular to irregular reflection of cylindrical converging shock waves over convex obstacles

    Science.gov (United States)

    Vignati, F.; Guardone, A.

    2017-11-01

    An analytical model for the evolution of regular reflections of cylindrical converging shock waves over circular-arc obstacles is proposed. The model based on the new (local) parameter, the perceived wedge angle, which substitutes the (global) wedge angle of planar surfaces and accounts for the time-dependent curvature of both the shock and the obstacle at the reflection point, is introduced. The new model compares fairly well with numerical results. Results from numerical simulations of the regular to Mach transition—eventually occurring further downstream along the obstacle—point to the perceived wedge angle as the most significant parameter to identify regular to Mach transitions. Indeed, at the transition point, the value of the perceived wedge angle is between 39° and 42° for all investigated configurations, whereas, e.g., the absolute local wedge angle varies in between 10° and 45° in the same conditions.

  17. Extended Jacobi Elliptic Function Rational Expansion Method and Its Application to (2+1)-Dimensional Stochastic Dispersive Long Wave System

    International Nuclear Information System (INIS)

    Song Lina; Zhang Hongqing

    2007-01-01

    In this work, by means of a generalized method and symbolic computation, we extend the Jacobi elliptic function rational expansion method to uniformly construct a series of stochastic wave solutions for stochastic evolution equations. To illustrate the effectiveness of our method, we take the (2+1)-dimensional stochastic dispersive long wave system as an example. We not only have obtained some known solutions, but also have constructed some new rational formal stochastic Jacobi elliptic function solutions.

  18. Transient difference solutions of the inhomogeneous wave equation - Simulation of the Green's function

    Science.gov (United States)

    Baumeister, K. J.

    1983-01-01

    A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.

  19. Transient difference solutions of the inhomogeneous wave equation: Simulation of the Green's function

    Science.gov (United States)

    Baumeiste, K. J.

    1983-01-01

    A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.

  20. Perfectly Matched Layer for the Wave Equation Finite Difference Time Domain Method

    Science.gov (United States)

    Miyazaki, Yutaka; Tsuchiya, Takao

    2012-07-01

    The perfectly matched layer (PML) is introduced into the wave equation finite difference time domain (WE-FDTD) method. The WE-FDTD method is a finite difference method in which the wave equation is directly discretized on the basis of the central differences. The required memory of the WE-FDTD method is less than that of the standard FDTD method because no particle velocity is stored in the memory. In this study, the WE-FDTD method is first combined with the standard FDTD method. Then, Berenger's PML is combined with the WE-FDTD method. Some numerical demonstrations are given for the two- and three-dimensional sound fields.

  1. Stochastic wave-function unravelling of the generalized Lindblad equation using correlated states

    International Nuclear Information System (INIS)

    Moodley, Mervlyn; Nsio Nzundu, T; Paul, S

    2012-01-01

    We perform a stochastic wave-function unravelling of the generalized Lindblad master equation using correlated states, a combination of the system state vectors and the environment population. The time-convolutionless projection operator method using correlated projection superoperators is applied to a two-state system, a qubit, that is coupled to an environment consisting of two energy bands which are both populated. These results are compared to the data obtained from Monte Carlo wave-function simulations based on the unravelling of the master equation. We also show a typical quantum trajectory and the average time evolution of the state vector on the Bloch sphere. (paper)

  2. Bifurcations of Exact Traveling Wave Solutions for (2+1)-Dimensional HNLS Equation

    International Nuclear Information System (INIS)

    Xu Yuanfen

    2012-01-01

    For the (2+1)-Dimensional HNLS equation, what are the dynamical behavior of its traveling wave solutions and how do they depend on the parameters of the systems? This paper will answer these questions by using the methods of dynamical systems. Ten exact explicit parametric representations of the traveling wave solutions are given. (general)

  3. Wave Tank Studies of Strong Modulation of Wind Ripples Due To Long Waves

    Science.gov (United States)

    Ermakov, S.; Sergievskaya, I.; Shchegolkov, Yu.

    Modulation of wind capillary-gravity ripples due to long waves has been studied in wave tank experiment at low wind speeds using Ka-band radar. The experiments were carried out both for clean water and the water surface covered with surfactant films. It is obtained that the modulation of radar signals is quite strong and can increase with surfactant concentration and fetch. It is shown that the hydrodynamic Modulation Transfer Function (MTF) calculated for free wind ripples and taking into account the kinematic (straining) effect, variations of the wind stress and variations of surfactant concentration strongly underestimates experimental MTF-values. The effect of strong modulation is assumed to be connected with nonlinear harmonics of longer dm-cm- scale waves - bound waves ("parasitic ripples"). The intensity of bound waves depends strongly on the amplitude of decimetre-scale waves, therefore even weak modulation of the dm-scale waves due to long waves results to strong ("cascade") modulation of bound waves. Modulation of the system of "free/bound waves" is estimated using results of wave tank studies of bound waves generation and is shown to be in quali- tative agreement with experiment. This work was supported by MOD, UK via DERA Winfrith (Project ISTC 1774P) and by RFBR (Project 02-05-65102).

  4. Antisymmetrized molecular dynamics of wave packets with stochastic incorporation of Vlasov equation

    International Nuclear Information System (INIS)

    Ono, Akira; Horiuchi, Hisashi.

    1996-01-01

    The first purpose of this report is to present an extended AMD model which can generally describe such minor branching processes by removing the restriction on the one-body distribution function. This is done not by generalizing the wave packets to arbitrary single-particle wave functions but by representing the diffused and/or deformed wave packet as an ensemble of Gaussian wave packets. In other words, stochastic displacements are given to the wave packets in phase space so that the ensemble-average of the time evolution of the one-body distribution function is essentially equivalent to the solution of Vlasov equation which does not have any restriction on the shape of wave packets. This new model is called AMD-V. Although AMD-V is equivalent to Vlasov equation in the instantaneous time evolution of the one-body distribution function for an AMD wave function, AMD-V describes the branching into channels and the fluctuation of the mean field which are caused by the spreading or the splitting of the single-particle wave function. The second purpose of this report is to show the drastic effect of this new stochastic process of wave packet splitting on the dynamics of heavy ion collisions, especially in the fragmentation mechanism. We take the 40 Ca + 40 Ca system at the incident energy 35 MeV/nucleon. It will be shown that the reproduction of data by the AMD-V calculation is surprisingly good. We will see that the effect of the wave packet diffusion is crucially important to remove the spurious binary feature of the AMD calculation and to enable the multi-fragment final state. (J.P.N.)

  5. Application of Modified G'/G-Expansion Method to Traveling Wave Solutions for Whitham-Broer-Kaup-Like Equations

    International Nuclear Information System (INIS)

    Zhou Yubin; Li Chao

    2009-01-01

    A modified G'/G-expansion method is presented to derive traveling wave solutions for a class of nonlinear partial differential equations called Whitham-Broer-Kaup-Like equations. As a result, the hyperbolic function solutions, trigonometric function solutions, and rational solutions with parameters to the equations are obtained. When the parameters are taken as special values the solitary wave solutions can be obtained. (general)

  6. Shot- and angle-domain wave-equation traveltime inversion of reflection data: Theory

    KAUST Repository

    Zhang, Sanzong

    2015-05-26

    The main difficulty with iterative waveform inversion is that it tends to get stuck in local minima associated with the waveform misfit function. To mitigate this problem and avoid the need to fit amplitudes in the data, we have developed a wave-equation method that inverts the traveltimes of reflection events, and so it is less prone to the local minima problem. Instead of a waveform misfit function, the penalty function was a crosscorrelation of the downgoing direct wave and the upgoing reflection wave at the trial image point. The time lag, which maximized the crosscorrelation amplitude, represented the reflection-traveltime residual (RTR) that was back projected along the reflection wavepath to update the velocity. Shot- and angle-domain crosscorrelation functions were introduced to estimate the RTR by semblance analysis and scanning. In theory, only the traveltime information was inverted and there was no need to precisely fit the amplitudes or assume a high-frequency approximation. Results with synthetic data and field records revealed the benefits and limitations of wave-equation reflection traveltime inversion.

  7. Shot- and angle-domain wave-equation traveltime inversion of reflection data: Theory

    KAUST Repository

    Zhang, Sanzong; Luo, Yi; Schuster, Gerard T.

    2015-01-01

    The main difficulty with iterative waveform inversion is that it tends to get stuck in local minima associated with the waveform misfit function. To mitigate this problem and avoid the need to fit amplitudes in the data, we have developed a wave-equation method that inverts the traveltimes of reflection events, and so it is less prone to the local minima problem. Instead of a waveform misfit function, the penalty function was a crosscorrelation of the downgoing direct wave and the upgoing reflection wave at the trial image point. The time lag, which maximized the crosscorrelation amplitude, represented the reflection-traveltime residual (RTR) that was back projected along the reflection wavepath to update the velocity. Shot- and angle-domain crosscorrelation functions were introduced to estimate the RTR by semblance analysis and scanning. In theory, only the traveltime information was inverted and there was no need to precisely fit the amplitudes or assume a high-frequency approximation. Results with synthetic data and field records revealed the benefits and limitations of wave-equation reflection traveltime inversion.

  8. Exponential decay for solutions to semilinear damped wave equation

    KAUST Repository

    Gerbi, Stéphane

    2011-10-01

    This paper is concerned with decay estimate of solutions to the semilinear wave equation with strong damping in a bounded domain. Intro- ducing an appropriate Lyapunov function, we prove that when the damping is linear, we can find initial data, for which the solution decays exponentially. This result improves an early one in [4].

  9. Application of the N/D-method to the Roy equations

    International Nuclear Information System (INIS)

    Heemskerk, A.C.

    1978-01-01

    The subject of this thesis is the study and numerical application of the Roy equations for elastic pion-pion scattering. These equations were introduced by S.M. Roy in 1971 and express the minimal requirements any ππ partial wave amplitude should satisfy, such as analyticity and crossing symmetry. When combined with the unitarity relations for the partial waves a complete system of equations (the Roy system) results valid in the low-energy region. The author has studied the existance and uniqueness question for the Roy system and developed successful strategies to solve the system by means of iteration. Several solutions are presented and discussed. The main ingredients in the present approach are a) the use of the N/D-method to regularize the singular Roy equations and implement unitarity and b) the introduction of various iteration methods which do not need any derivatives to solve the resulting nonlinear system of equations numerically. (Auth.)

  10. Wave-Breaking Phenomena and Existence of Peakons for a Generalized Compressible Elastic-Rod Equation

    Directory of Open Access Journals (Sweden)

    Xiaolian Ai

    2014-01-01

    Full Text Available Consideration in this paper is the Cauchy problem of a generalized hyperelastic-rod wave equation. We first derive a wave-breaking mechanism for strong solutions, which occurs in finite time for certain initial profiles. In addition, we determine the existence of some new peaked solitary wave solutions.

  11. Wave equations on a de Sitter fiber bundle. [Semiclassical wave function, bundle space, L-S coupling

    Energy Technology Data Exchange (ETDEWEB)

    Drechsler, W [Max-Planck-Institut fuer Physik und Astrophysik, Muenchen (F.R. Germany)

    1975-01-01

    A gauge theory of strong interaction is developed based on fields defined on a fiber bundle. The structural group of the bundle is taken to be the Lsub(4,1) de Sitter group. An internal variable xi, varying in the fiber over a space-time point x, is introduced as a means to describe - with the help of a semiclassical wave function psi(x,xi) defined on the bundle space - the internal structure of extended hadrons in a framework using differential geometric techniques. Three basic nonlinear wave equations for psi(x,xi) are established which are of integro-differential type. The nonlinear coupling terms in these de Sitter gauge invariant equations represent physically a generalized spin orbit coupling or a generalized spin coupling for the motion taking place in the fiber. The motivation for using a bigger space for the definition of hadronic matter wave functions as well as the implications of this geometric approach to strong interaction physics is discussed in detail, in particular with respect to the problem of hadronic constituents. The proposed fiber bundle formalism allows a dynamical description of extended structures for hadrons without implying the necessity of introducing any constituents.

  12. Modified method of simplest equation: Powerful tool for obtaining exact and approximate traveling-wave solutions of nonlinear PDEs

    Science.gov (United States)

    Vitanov, Nikolay K.

    2011-03-01

    We discuss the class of equations ∑i,j=0mAij(u){∂iu}/{∂ti}∂+∑k,l=0nBkl(u){∂ku}/{∂xk}∂=C(u) where Aij( u), Bkl( u) and C( u) are functions of u( x, t) as follows: (i) Aij, Bkl and C are polynomials of u; or (ii) Aij, Bkl and C can be reduced to polynomials of u by means of Taylor series for small values of u. For these two cases the above-mentioned class of equations consists of nonlinear PDEs with polynomial nonlinearities. We show that the modified method of simplest equation is powerful tool for obtaining exact traveling-wave solution of this class of equations. The balance equations for the sub-class of traveling-wave solutions of the investigated class of equations are obtained. We illustrate the method by obtaining exact traveling-wave solutions (i) of the Swift-Hohenberg equation and (ii) of the generalized Rayleigh equation for the cases when the extended tanh-equation or the equations of Bernoulli and Riccati are used as simplest equations.

  13. Four-Wave Mixing of Gigawatt Power, Long-Wave Infrared Radiation in Gases and Semiconductors

    Science.gov (United States)

    Pigeon, Jeremy James

    The nonlinear optics of gigawatt power, 10 microm, 3 and 200 ps long pulses propagating in gases and semiconductors has been studied experimentally and numerically. In this work, the development of a high-repetition rate, picosecond, CO2 laser system has enabled experiments using peak intensities in the range of 1-10 GW/cm2, approximately one thousand times greater than previous nonlinear optics experiments in the long-wave infrared (LWIR) spectral region. The first measurements of the nonlinear refractive index of the atomic and molecular gases Kr, Xe, N2, O2 and the air at a wavelength near 10 microm were accomplished by studying the four-wave mixing (FWM) of dual-wavelength, 200 ps CO2 laser pulses. These measurements indicate that the nonlinearities of the diatomic molecules N2, O2 and the air are dominated by the molecular contribution to the nonlinear refractive index. Supercontinuum (SC) generation covering the infrared spectral range, from 2-20 microm, was realized by propagating 3 ps, 10 microm pulses in an approximately 7 cm long, Cr-doped GaAs crystal. Temporal measurements of the SC radiation show that pulse splitting accompanies the generation of such broadband light in GaAs. The propagation of 3 ps, 10 microm pulses in GaAs was studied numerically by solving the Generalized Nonlinear Schrodinger Equation (GNLSE). These simulations, combined with analytic estimates, were used to determine that stimulated Raman scattering combined with a modulational instability caused by the propagation of intense LWIR radiation in the negative group velocity dispersion region of GaAs are responsible for the SC generation process. The multiple FWM of a 106 GHz, 200 ps CO2 laser beat-wave propagating in GaAs was used to generate a broadband FWM spectrum that was compressed by the negative group velocity dispersion of GaAs and NaCl crystals to form trains of high-power, picosecond pulses at a wavelength near 10 microm. Experimental FWM spectra obtained using 165 and 882

  14. Combined solitary-wave solution for coupled higher-order nonlinear Schroedinger equations

    International Nuclear Information System (INIS)

    Tian Jinping; Tian Huiping; Li Zhonghao; Zhou Guosheng

    2004-01-01

    Coupled nonlinear Schroedinger equations model several interesting physical phenomena. We used a trigonometric function transform method based on a homogeneous balance to solve the coupled higher-order nonlinear Schroedinger equations. We obtained four pairs of exact solitary-wave solutions including a dark and a bright-soliton pair, a bright- and a dark-soliton pair, a bright- and a bright-soliton pair, and the last pair, a combined bright-dark-soliton pair

  15. Regularity criterion for solutions to the Navier Stokes equations in the whole 3D space based on two vorticity components

    Czech Academy of Sciences Publication Activity Database

    Guo, Z.; Kučera, P.; Skalák, Zdeněk

    2018-01-01

    Roč. 458, č. 1 (2018), s. 755-766 ISSN 0022-247X R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985874 Keywords : Navier Stokes equations * conditional regularity * regularity criteria * vorticity * Besov spaces * bony decomposition Subject RIV: BA - General Mathematics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 1.064, year: 2016

  16. Exact traveling wave solutions of the bbm and kdv equations using (G'/G)-expansion method

    International Nuclear Information System (INIS)

    Saddique, I.; Nazar, K.

    2009-01-01

    In this paper, we construct the traveling wave solutions involving parameters of the Benjamin Bona-Mahony (BBM) and KdV equations in terms of the hyperbolic, trigonometric and rational functions by using the (G'/G)-expansion method, where G = G(zeta) satisfies a second order linear ordinary differential equation. When the parameters are taken special values, the Solitary was are derived from the traveling waves. (author)

  17. Dispersive solitary wave solutions of Kadomtsev-Petviashvili and modified Kadomtsev-Petviashvili dynamical equations in unmagnetized dust plasma

    Science.gov (United States)

    Seadawy, A. R.; El-Rashidy, K.

    2018-03-01

    The Kadomtsev-Petviashvili (KP) and modified KP equations are two of the most universal models in nonlinear wave theory, which arises as a reduction of system with quadratic nonlinearity which admit weakly dispersive waves. The generalized extended tanh method and the F-expansion method are used to derive exact solitary waves solutions of KP and modified KP equations. The region of solutions are displayed graphically.

  18. Integrable discretizations for the short-wave model of the Camassa-Holm equation

    International Nuclear Information System (INIS)

    Feng Baofeng; Maruno, Ken-ichi; Ohta, Yasuhiro

    2010-01-01

    The link between the short-wave model of the Camassa-Holm equation (SCHE) and bilinear equations of the two-dimensional Toda lattice equation is clarified. The parametric form of the N-cuspon solution of the SCHE in Casorati determinant is then given. Based on the above finding, integrable semi-discrete and full-discrete analogues of the SCHE are constructed. The determinant solutions of both semi-discrete and fully discrete analogues of the SCHE are also presented.

  19. Investigation of Solitary wave solutions for Vakhnenko-Parkes equation via exp-function and Exp(-ϕ(ξ))-expansion method.

    Science.gov (United States)

    Roshid, Harun-Or; Kabir, Md Rashed; Bhowmik, Rajandra Chadra; Datta, Bimal Kumar

    2014-01-01

    In this paper, we have described two dreadfully important methods to solve nonlinear partial differential equations which are known as exp-function and the exp(-ϕ(ξ)) -expansion method. Recently, there are several methods to use for finding analytical solutions of the nonlinear partial differential equations. The methods are diverse and useful for solving the nonlinear evolution equations. With the help of these methods, we are investigated the exact travelling wave solutions of the Vakhnenko- Parkes equation. The obtaining soliton solutions of this equation are described many physical phenomena for weakly nonlinear surface and internal waves in a rotating ocean. Further, three-dimensional plots of the solutions such as solitons, singular solitons, bell type solitary wave i.e. non-topological solitons solutions and periodic solutions are also given to visualize the dynamics of the equation.

  20. Application of the Exp-function method to the equal-width wave equation

    International Nuclear Information System (INIS)

    Biazar, J; Ayati, Z

    2008-01-01

    In this paper, the Exp-function method is used to find an exact solution of the equal-width wave (EW) equation. The method is straightforward and concise, and its applications are promising. It is shown that the Exp-function method, with the help of symbolic computation, provides a very effective and powerful mathematical tool for solving the EW equation.

  1. Boundary Observability and Stabilization for Westervelt Type Wave Equations without Interior Damping

    International Nuclear Information System (INIS)

    Kaltenbacher, Barbara

    2010-01-01

    In this paper we show boundary observability and boundary stabilizability by linear feedbacks for a class of nonlinear wave equations including the undamped Westervelt model used in nonlinear acoustics. We prove local existence for undamped generalized Westervelt equations with homogeneous Dirichlet boundary conditions as well as global existence and exponential decay with absorbing type boundary conditions.

  2. Analysis and computation of the elastic wave equation with random coefficients

    KAUST Repository

    Motamed, Mohammad; Nobile, Fabio; Tempone, Raul

    2015-01-01

    We consider the stochastic initial-boundary value problem for the elastic wave equation with random coefficients and deterministic data. We propose a stochastic collocation method for computing statistical moments of the solution or statistics

  3. Finite Amplitude Electron Plasma Waves in a Cylindrical Waveguide

    DEFF Research Database (Denmark)

    Juul Rasmussen, Jens

    1978-01-01

    The nonlinear behaviour of the electron plasma wave propagating in a cylindrical plasma waveguide immersed in an infinite axial magnetic field is investigated using the Krylov-Bogoliubov-Mitropolsky perturbation method, by means of which is deduced the nonlinear Schrodinger equation governing...... the long-time slow modulation of the wave amplitude. From this equation the amplitude-dependent frequency and wavenumber shifts are calculated, and it is found that the electron waves with short wavelengths are modulationally unstable with respect to long-wavelength, low-frequency perturbations...

  4. Solitary wave for a nonintegrable discrete nonlinear Schrödinger equation in nonlinear optical waveguide arrays

    Science.gov (United States)

    Ma, Li-Yuan; Ji, Jia-Liang; Xu, Zong-Wei; Zhu, Zuo-Nong

    2018-03-01

    We study a nonintegrable discrete nonlinear Schrödinger (dNLS) equation with the term of nonlinear nearest-neighbor interaction occurred in nonlinear optical waveguide arrays. By using discrete Fourier transformation, we obtain numerical approximations of stationary and travelling solitary wave solutions of the nonintegrable dNLS equation. The analysis of stability of stationary solitary waves is performed. It is shown that the nonlinear nearest-neighbor interaction term has great influence on the form of solitary wave. The shape of solitary wave is important in the electric field propagating. If we neglect the nonlinear nearest-neighbor interaction term, much important information in the electric field propagating may be missed. Our numerical simulation also demonstrates the difference of chaos phenomenon between the nonintegrable dNLS equation with nonlinear nearest-neighbor interaction and another nonintegrable dNLS equation without the term. Project supported by the National Natural Science Foundation of China (Grant Nos. 11671255 and 11701510), the Ministry of Economy and Competitiveness of Spain (Grant No. MTM2016-80276-P (AEI/FEDER, EU)), and the China Postdoctoral Science Foundation (Grant No. 2017M621964).

  5. Measuring the neutron star equation of state with gravitational wave observations

    International Nuclear Information System (INIS)

    Read, Jocelyn S.; Markakis, Charalampos; Creighton, Jolien D. E.; Friedman, John L.; Shibata, Masaru; Uryu, Koji

    2009-01-01

    We report the results of a first study that uses numerical simulations to estimate the accuracy with which one can use gravitational wave observations of double neutron-star inspiral to measure parameters of the neutron-star equation of state. The simulations use the evolution and initial-data codes of Shibata and Uryu to compute the last several orbits and the merger of neutron stars, with matter described by a parametrized equation of state. Previous work suggested the use of an effective cutoff frequency to place constraints on the equation of state. We find, however, that greater accuracy is obtained by measuring departures from the point-particle limit of the gravitational waveform produced during the late inspiral. As the stars approach their final plunge and merger, the gravitational wave phase accumulates more rapidly for smaller values of the neutron-star compactness (the ratio of the mass of the neutron-star to its radius). We estimate that realistic equations of state will lead to gravitational waveforms that are distinguishable from point-particle inspirals at an effective distance (the distance to an optimally oriented and located system that would produce an equivalent waveform amplitude) of 100 Mpc or less. As Lattimer and Prakash observed, neutron-star radius is closely tied to the pressure at density not far above nuclear. Our results suggest that broadband gravitational wave observations at frequencies between 500 and 1000 Hz will constrain this pressure, and we estimate the accuracy with which it can be measured. Related first estimates of radius measurability show that the radius can be determined to an accuracy of δR∼1 km at 100 Mpc.

  6. Stochastic generation of continuous wave spectra

    DEFF Research Database (Denmark)

    Trulsen, J.; Dysthe, K. B.; Pécseli, Hans

    1983-01-01

    Wave packets of electromagnetic or Langmuir waves trapped in a well between oscillating reflectors are considered. An equation for the temporal evolution of the probability distribution for the carrier wave number is derived, and solved analytically in terms of moments in the limits of long...

  7. Travelling wave solutions in a class of generalized Korteweg-de Vries equation

    International Nuclear Information System (INIS)

    Shen Jianwei; Xu Wei

    2007-01-01

    In this paper, we consider a new generalization of KdV equation u t = u x u l-2 + α[2u xxx u p + 4pu p-1 u x u xx + p(p - 1)u p-2 (u x ) 3 ] and investigate its bifurcation of travelling wave solutions. From the above analysis, we know that there exists compacton and cusp waves in the system. We explain the reason that these non-smooth travelling wave solution arise by using the bifurcation theory

  8. Conservation Laws and Traveling Wave Solutions of a Generalized Nonlinear ZK-BBM Equation

    Directory of Open Access Journals (Sweden)

    Khadijo Rashid Adem

    2014-01-01

    Full Text Available We study a generalized two-dimensional nonlinear Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZK-BBM equation, which is in fact Benjamin-Bona-Mahony equation formulated in the ZK sense. Conservation laws for this equation are constructed by using the new conservation theorem due to Ibragimov and the multiplier method. Furthermore, traveling wave solutions are obtained by employing the (G'/G-expansion method.

  9. Solitary wave solutions of the fourth order Boussinesq equation through the exp(-Ф(η))-expansion method.

    Science.gov (United States)

    Akbar, M Ali; Hj Mohd Ali, Norhashidah

    2014-01-01

    The exp(-Ф(η))-expansion method is an ascending method for obtaining exact and solitary wave solutions for nonlinear evolution equations. In this article, we implement the exp(-Ф(η))-expansion method to build solitary wave solutions to the fourth order Boussinesq equation. The procedure is simple, direct and useful with the help of computer algebra. By using this method, we obtain solitary wave solutions in terms of the hyperbolic functions, the trigonometric functions and elementary functions. The results show that the exp(-Ф(η))-expansion method is straightforward and effective mathematical tool for the treatment of nonlinear evolution equations in mathematical physics and engineering. 35C07; 35C08; 35P99.

  10. Assessment of thermodynamic parameters of plasma shock wave

    International Nuclear Information System (INIS)

    Vasileva, O V; Isaev, Yu N; Budko, A A; Filkov, A I

    2014-01-01

    The work is devoted to the solution of the one-dimensional equation of hydraulic gas dynamics for the coaxial magneto plasma accelerator by means of Lax-Wendroff modified algorithm with optimum choice of the regularization parameter artificial viscosity. Replacement of the differential equations containing private derivatives is made by finite difference method. Optimum parameter of regularization artificial viscosity is added using the exact known decision of Soda problem. The developed algorithm of thermodynamic parameter calculation in a braking point is proved. Thermodynamic parameters of a shock wave in front of the plasma piston of the coaxial magneto plasma accelerator are calculated on the basis of the offered algorithm. Unstable high-frequency fluctuations are smoothed using modeling and that allows narrowing the ambiguity area. Results of calculation of gas dynamic parameters in a point of braking coincide with literary data. The chart 3 shows the dynamics of change of speed and thermodynamic parameters of a shock wave such as pressure, density and temperature just before the plasma piston

  11. Invariant Solutions for a Class of Perturbed Nonlinear Wave Equations

    Directory of Open Access Journals (Sweden)

    Waheed A. Ahmed

    2017-11-01

    Full Text Available Approximate symmetries of a class of perturbed nonlinear wave equations are computed using two newly-developed methods. Invariant solutions associated with the approximate symmetries are constructed for both methods. Symmetries and solutions are compared through discussing the advantages and disadvantages of each method.

  12. An entropy regularization method applied to the identification of wave distribution function for an ELF hiss event

    Science.gov (United States)

    Prot, Olivier; SantolíK, OndřEj; Trotignon, Jean-Gabriel; Deferaudy, Hervé

    2006-06-01

    An entropy regularization algorithm (ERA) has been developed to compute the wave-energy density from electromagnetic field measurements. It is based on the wave distribution function (WDF) concept. To assess its suitability and efficiency, the algorithm is applied to experimental data that has already been analyzed using other inversion techniques. The FREJA satellite data that is used consists of six spectral matrices corresponding to six time-frequency points of an ELF hiss-event spectrogram. The WDF analysis is performed on these six points and the results are compared with those obtained previously. A statistical stability analysis confirms the stability of the solutions. The WDF computation is fast and without any prespecified parameters. The regularization parameter has been chosen in accordance with the Morozov's discrepancy principle. The Generalized Cross Validation and L-curve criterions are then tentatively used to provide a fully data-driven method. However, these criterions fail to determine a suitable value of the regularization parameter. Although the entropy regularization leads to solutions that agree fairly well with those already published, some differences are observed, and these are discussed in detail. The main advantage of the ERA is to return the WDF that exhibits the largest entropy and to avoid the use of a priori models, which sometimes seem to be more accurate but without any justification.

  13. Characteristics of the solitary waves and rogue waves with interaction phenomena in a (2 + 1)-dimensional Breaking Soliton equation

    Science.gov (United States)

    Hossen, Md. Belal; Roshid, Harun-Or; Ali, M. Zulfikar

    2018-05-01

    Under inquisition in this paper is a (2 + 1)-dimensional Breaking Soliton equation, which can describe various nonlinear scenarios in fluid dynamics. Using the Bell polynomials, some proficient auxiliary functions are offered to apparently construct its bilinear form and corresponding soliton solutions which are different from the previous literatures. Moreover, a direct method is used to construct its rogue wave and solitary wave solutions using particular auxiliary function with the assist of bilinear formalism. Finally, the interactions between solitary waves and rogue waves are offered with a complete derivation. These results enhance the variety of the dynamics of higher dimensional nonlinear wave fields related to mathematical physics and engineering.

  14. New exact travelling wave solutions of generalised sinh- Gordon and (2 + 1-dimensional ZK-BBM equations

    Directory of Open Access Journals (Sweden)

    Sachin Kumar

    2012-10-01

    Full Text Available Exact travelling wave solutions have been established for generalised sinh-Gordon andgeneralised (2+1 dimensional ZK-BBM equations by using GG      expansion method whereG  G( satisfies a second-order linear ordinary differential equation. The travelling wave solutionsare expressed by hyperbolic, trigonometric and rational functions.

  15. Extended common-image-point gathers for anisotropic wave-equation migration

    KAUST Repository

    Sava, Paul C.

    2010-01-01

    In regions characterized by complex subsurface structure, wave-equation depth migration is a powerful tool for accurately imaging the earth’s interior. The quality of the final image greatly depends on the quality of the model which includes anisotropy parameters (Gray et al., 2001). In particular, it is important to construct subsurface velocity models using techniques that are consistent with the methods used for imaging. Generally speaking, there are two possible strategies for velocity estimation from surface seismic data in the context of wavefield-based imaging (Sava et al., 2010). One possibility is to formulate an objective function in the data space, prior to migration, by matching the recorded data with simulated data. Techniques in this category are known by the name of waveform inversion. Another possibility is to formulate an objective function in the image space, after migration, by measuring and correcting image features that indicate model inaccuracies. Techniques in this category are known as wave-equation migration velocity analysis (MVA).

  16. Soliton on a cnoidal wave background in the coupled nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Shin, H J

    2004-01-01

    An application of the Darboux transformation on a cnoidal wave background in the coupled nonlinear Schroedinger equation gives a new solution which describes a soliton moving on a cnoidal wave. This is a generalized version of the previously known soliton solutions of dark-bright pair. Here a dark soliton resides on a cnoidal wave instead of on a constant background. It also exhibits a new type of soliton solution in a self-focusing medium, which describes a breakup of a generalized dark-bright pair into another generalized dark-bright pair and an 'oscillating' soliton. We calculate the shift of the crest of the cnoidal wave along a soliton and the moving direction of the soliton on a cnoidal wave

  17. Rogue waves in the multicomponent Mel'nikov system and ...

    Indian Academy of Sciences (India)

    By virtue of the bilinear method and the KP hierarchy reduction technique, exact explicit rational solutions of the multicomponent Mel'nikov equation and the multicomponent Schrödinger–Boussinesq equation are constructed, which contain multicomponent short waves and single-component long wave. For the ...

  18. Integral representations of solutions of the wave equation based on relativistic wavelets

    International Nuclear Information System (INIS)

    Perel, Maria; Gorodnitskiy, Evgeny

    2012-01-01

    A representation of solutions of the wave equation with two spatial coordinates in terms of localized elementary ones is presented. Elementary solutions are constructed from four solutions with the help of transformations of the affine Poincaré group, i.e. with the help of translations, dilations in space and time and Lorentz transformations. The representation can be interpreted in terms of the initial-boundary value problem for the wave equation in a half-plane. It gives the solution as an integral representation of two types of solutions: propagating localized solutions running away from the boundary under different angles and packet-like surface waves running along the boundary and exponentially decreasing away from the boundary. Properties of elementary solutions are discussed. A numerical investigation of coefficients of the decomposition is carried out. An example of the decomposition of the field created by sources moving along a line with different speeds is considered, and the dependence of coefficients on speeds of sources is discussed. (paper)

  19. On a correspondence between regular and non-regular operator monotone functions

    DEFF Research Database (Denmark)

    Gibilisco, P.; Hansen, Frank; Isola, T.

    2009-01-01

    We prove the existence of a bijection between the regular and the non-regular operator monotone functions satisfying a certain functional equation. As an application we give a new proof of the operator monotonicity of certain functions related to the Wigner-Yanase-Dyson skew information....

  20. Amplitude equations for a sub-diffusive reaction-diffusion system

    International Nuclear Information System (INIS)

    Nec, Y; Nepomnyashchy, A A

    2008-01-01

    A sub-diffusive reaction-diffusion system with a positive definite memory operator and a nonlinear reaction term is analysed. Amplitude equations (Ginzburg-Landau type) are derived for short wave (Turing) and long wave (Hopf) bifurcation points