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.

Application of the graphical unitary group approach to the energy second derivative for CI wave functions via the coupled perturbed CI equations

International Nuclear Information System (INIS)

Fox, D.J.

1983-10-01

Analytic derivatives of the potential energy for Self-Consistent-Field (SCF) wave functions have been developed in recent years and found to be useful tools. The first derivative for configuration interaction (CI) wave functions is also available. This work details the extension of analytic methods to energy second derivatives for CI wave functions. The principal extension required for second derivatives is evaluation of the first order change in the CI wave function with respect to a nuclear perturbation. The shape driven graphical unitary group approach (SDGUGA) direct CI program was adapted to evaluate this term via the coupled-perturbed CI equations. Several iterative schemes are compared for use in solving these equations. The pilot program makes no use of molecular symmetry but the timing results show that utilization of molecular symmetry is desirable. The principles for defining and solving a set of symmetry adapted equations are discussed. Evaluation of the second derivative also requires the solution of the second order coupled-perturbed Hartree-Fock equations to obtain the correction to the molecular orbitals due to the nuclear perturbation. This process takes a consistently higher percentage of the computation time than for the first order equations alone and a strategy for its reduction is discussed

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

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

Mode coupling of electron plasma waves

International Nuclear Information System (INIS)

Harte, J.A.

1975-01-01

The driven coupled mode equations are derived for a two fluid, unequal temperature (T/sub e/ much greater than T/sub i/) plasma in the one-dimensional, electrostatic model and applied to the coupling of electron plasma waves. It is assumed that the electron to ion mass ratio identical with m/sub e/M/sub i// much less than 1 and eta 2 /sub ko/k lambda/sub De/ less than 1 where eta 2 /sub ko/ is the pump wave's power normalized to the plasma thermal energy, k the mode wave number and lambda/sub De/ the electron Debye length. Terms up to quadratic in pump power are retained. The equations describe the linear plasma modes oscillating at the wave number k and at ω/sub ek/, the Bohn Gross frequency, and at Ω/sub k/, the ion acoustic frequency, subject to the damping rates ν/sub ek/ and ν/sub ik/ for electrons and ions and their interactions due to intense high frequency waves E/sub k//sup l/. n/sub o/ is the background density, n/sub ik/ the fluctuating ion density, ω/sub pe/ the plasma frequency

Travelling Wave Solutions of Coupled Burger’s Equations of Time-Space Fractional Order by Novel (Gʹ/G-Expansion Method

Directory of Open Access Journals (Sweden)

Rashida Hussain

2017-04-01

Full Text Available In this paper, Novel (Gʹ/G-expansion method is used to find new generalized exact travelling wave solutions of fractional order coupled Burger’s equations in terms of trigonometric functions, rational functions and hyperbolic functions with arbitrary parameters. For the conversion of the partial differential equation to the ordinary differential equation, complex transformation method is used. Novel (Gʹ/G-expansion method is very effective and provides a powerful mathematical tool to solve nonlinear equations. Moreover, for the representation of these exact solutions we have plotted graphs for different values of parameters which were in travelling waveform.

Scalar fields nonminimally coupled to pp waves

International Nuclear Information System (INIS)

Ayon-Beato, Eloy; Hassaiene, Mokhtar

2005-01-01

Here, we report pp waves configurations of three-dimensional gravity for which a scalar field nonminimally coupled to them acts as a source. In absence of self-interaction the solutions are gravitational plane waves with a profile fixed in terms of the scalar wave. In the self-interacting case, only power-law potentials parameterized by the nonminimal coupling constant are allowed by the field equations. In contrast with the free case the self-interacting scalar field does not behave like a wave since it depends only on the wave-front coordinate. We address the same problem when gravitation is governed by topologically massive gravity and the source is a free scalar field. From the pp waves derived in this case, we obtain at the zero topological mass limit, new pp waves solutions of conformal gravity for any arbitrary value of the nonminimal coupling parameter. Finally, we extend these solutions to the self-interacting case of conformal gravity

Lax pair and exact solutions of a discrete coupled system related to coupled KdV and coupled mKdV equations

International Nuclear Information System (INIS)

Liu Ping; Jia Man; Lou Senyue

2007-01-01

A modified Korteweg-de Vries (mKdV) lattice is also found to be a discrete Korteweg-de Vries (KdV) equation in this paper. The Lax pair for the discrete equation is found with the help of the Lax pair for a similar discrete equation. A Lax-integrable coupled extension of the lattice is posed, which is a common discrete version of both the coupled KdV and coupled mKdV systems. Some rational expansions of the Jacobian elliptic, trigonometric and hyperbolic functions are used to construct cnoidal waves, negaton and positon solutions of the discrete coupled system

Solitary waves for a coupled nonlinear Schrodinger system with dispersion management

Directory of Open Access Journals (Sweden)

Panayotis Panayotaros

2010-08-01

Full Text Available We consider a system of coupled nonlinear Schrodinger equations with periodically varying dispersion coefficient that arises in the context of fiber-optics communication. We use Lions's Concentration Compactness principle to show the existence of standing waves with prescribed L^2 norm in an averaged equation that approximates the coupled system. We also use the Mountain Pass Lemma to prove the existence of standing waves with prescribed frequencies.

Coupled wave equations theory of surface-enhanced femtosecond stimulated Raman scattering.

Science.gov (United States)

McAnally, Michael O; McMahon, Jeffrey M; Van Duyne, Richard P; Schatz, George C

2016-09-07

We present a coupled wave semiclassical theory to describe plasmonic enhancement effects in surface-enhanced femtosecond stimulated Raman scattering (SE-FSRS). A key result is that the plasmon enhanced fields which drive the vibrational equation of motion for each normal mode results in dispersive lineshapes in the SE-FSRS spectrum. This result, which reproduces experimental lineshapes, demonstrates that plasmon-enhanced stimulated Raman methods provide unique sensitivity to a plasmonic response. Our derived SE-FSRS theory shows a plasmonic enhancement of |gpu|(2)ImχR(ω)gst (2)/ImχR(ω), where |gpu|(2) is the absolute square of the plasmonic enhancement from the Raman pump, χR(ω) is the Raman susceptibility, and gst is the plasmonic enhancement of the Stokes field in SE-FSRS. We conclude with a discussion on potential future experimental and theoretical directions for the field of plasmonically enhanced coherent Raman scattering.

Some remarks on coherent nonlinear coupling of waves in plasmas

International Nuclear Information System (INIS)

Wilhelmsson, H.

1976-01-01

The analysis of nonlinear processes in plasma physics has given rise to a basic set of coupled equations. These equations describe the coherent nonlinear evolution of plasma waves. In this paper various possibilities of analysing these equations are discussed and inherent difficulties in the description of nonlinear interactions between different types of waves are pointed out. Specific examples of stimulated excitation of waves are considered. These are the parametric excitation of hybrid resonances in hot magnetized multi-ion component plasma and laser-plasma interactions. (B.D.)

A polynomial expansion method and its application in the coupled Zakharov-Kuznetsov equations

International Nuclear Information System (INIS)

Huang Wenhua

2006-01-01

A polynomial expansion method is presented to solve nonlinear evolution equations. Applying this method, the coupled Zakharov-Kuznetsov equations in fluid system are studied and many exact travelling wave solutions are obtained. These solutions include solitary wave solutions, periodic solutions and rational type solutions

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

Novel method for solution of coupled radial Schrödinger equations

International Nuclear Information System (INIS)

Ershov, S. N.; Vaagen, J. S.; Zhukov, M. V.

2011-01-01

One of the major problems in numerical solution of coupled differential equations is the maintenance of linear independence for different sets of solution vectors. A novel method for solution of radial Schrödinger equations is suggested. It consists of rearrangement of coupled equations in a way that is appropriate to avoid usual numerical instabilities associated with components of the wave function in their classically forbidden regions. Applications of the new method for nuclear structure calculations within the hyperspherical harmonics approach are given.

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.

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.

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

On the Painleve integrability, periodic wave solutions and soliton solutions of generalized coupled higher-order nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Xu Guiqiong; Li Zhibin

2005-01-01

It is proven that generalized coupled higher-order nonlinear Schroedinger equations possess the Painleve property for two particular choices of parameters, using the Weiss-Tabor-Carnevale method and Kruskal's simplification. Abundant families of periodic wave solutions are obtained by using the Jacobi elliptic function expansion method with the assistance of symbolic manipulation system, Maple. It is also shown that these solutions exactly degenerate to bright soliton, dark soliton and mixed dark and bright soliton solutions with physical interests

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

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

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.

Coulomb singularities in scattering wave functions of spin-orbit-coupled states

International Nuclear Information System (INIS)

Bogdanski, P.; Ouerdane, H.

2011-01-01

We report on our analysis of the Coulomb singularity problem in the frame of the coupled channel scattering theory including spin-orbit interaction. We assume that the coupling between the partial wave components involves orbital angular momenta such that Δl= 0, ±2. In these conditions, the two radial functions, components of a partial wave associated to two values of the angular momentum l, satisfy a system of two second-order ordinary differential equations. We examine the difficulties arising in the analysis of the behavior of the regular solutions near the origin because of this coupling. First, we demonstrate that for a singularity of the first kind in the potential, one of the solutions is not amenable to a power series expansion. The use of the Lippmann-Schwinger equations confirms this fact: a logarithmic divergence arises at the second iteration. To overcome this difficulty, we introduce two auxilliary functions which, together with the two radial functions, satisfy a system of four first-order differential equations. The reduction of the order of the differential system enables us to use a matrix-based approach, which generalizes the standard Frobenius method. We illustrate our analysis with numerical calculations of coupled scattering wave functions in a solid-state system.

Local control of globally competing patterns in coupled Swift-Hohenberg equations

Science.gov (United States)

Becker, Maximilian; Frenzel, Thomas; Niedermayer, Thomas; Reichelt, Sina; Mielke, Alexander; Bär, Markus

2018-04-01

We present analytical and numerical investigations of two anti-symmetrically coupled 1D Swift-Hohenberg equations (SHEs) with cubic nonlinearities. The SHE provides a generic formulation for pattern formation at a characteristic length scale. A linear stability analysis of the homogeneous state reveals a wave instability in addition to the usual Turing instability of uncoupled SHEs. We performed weakly nonlinear analysis in the vicinity of the codimension-two point of the Turing-wave instability, resulting in a set of coupled amplitude equations for the Turing pattern as well as left- and right-traveling waves. In particular, these complex Ginzburg-Landau-type equations predict two major things: there exists a parameter regime where multiple different patterns are stable with respect to each other and that the amplitudes of different patterns interact by local mutual suppression. In consequence, different patterns can coexist in distinct spatial regions, separated by localized interfaces. We identified specific mechanisms for controlling the position of these interfaces, which distinguish what kinds of patterns the interface connects and thus allow for global pattern selection. Extensive simulations of the original SHEs confirm our results.

Nonlinear steady-state coupling of LH waves

International Nuclear Information System (INIS)

Ko, K.; Krapchev, V.B.

1981-02-01

The coupling of lower hybrid waves at the plasma edge by a two waveguide array with self-consistent density modulation is solved numerically. For a linear density profile, the governing nonlinear Klein-Gordon equation for the electric field can be written as a system of nonlinearly modified Airy equations in Fourier k/sub z/-space. Numerical solutions to the nonlinear system satisfying radiation condition are obtained. Spectra broadening and modifications to resonance cone trajectories are observed with increase of incident power

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

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.

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.

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.

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

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

Bifurcation analysis for ion acoustic waves in a strongly coupled plasma including trapped electrons

Science.gov (United States)

El-Labany, S. K.; El-Taibany, W. F.; Atteya, A.

2018-02-01

The nonlinear ion acoustic wave propagation in a strongly coupled plasma composed of ions and trapped electrons has been investigated. The reductive perturbation method is employed to derive a modified Korteweg-de Vries-Burgers (mKdV-Burgers) equation. To solve this equation in case of dissipative system, the tangent hyperbolic method is used, and a shock wave solution is obtained. Numerical investigations show that, the ion acoustic waves are significantly modified by the effect of polarization force, the trapped electrons and the viscosity coefficients. Applying the bifurcation theory to the dynamical system of the derived mKdV-Burgers equation, the phase portraits of the traveling wave solutions of both of dissipative and non-dissipative systems are analyzed. The present results could be helpful for a better understanding of the waves nonlinear propagation in a strongly coupled plasma, which can be produced by photoionizing laser-cooled and trapped electrons [1], and also in neutron stars or white dwarfs interior.

Wave Propagation of Coupled Modes in the DNA Double Helix

International Nuclear Information System (INIS)

Tabi, Conrad B.; Mohamadou, Alidou; Kofane, Timoleon C.

2010-06-01

The dynamics of waves propagating along the DNA molecule is described by the coupled nonlinear Schroedinger equations. We consider both the single and the coupled nonlinear excitation modes, and we discuss their biological implications. Furthermore, the characteristics of the coupled mode solution are discussed and we show that such a solution can describe the local opening observed within the transcription and the replication phenomena. (author)

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.)

Tokamak wave coupling and heating in the ICRF

International Nuclear Information System (INIS)

Romero, H.; Scharer, J.; Sund, R.

1983-01-01

The authors consider wave propagation in the vicinity of the Ion Cyclotron Range of Frequencies (ICRF) in general tokamak geometries. The problem of wave coupling by means of waveguides is addressed. In particular, the reflection coefficient for a simple TE 10 waveguide is obtained by taking into account both the z and y spectrum of the launcher. In order to take into account spatial gradients in the plasma medium, they use a one-dimensional slab model of the plasma. Good coupling and heating results are obtained for the first few harmonics for sufficiently weak edge density gradient and > about 1 keV core temperatures. To analyze the heating of the plasma interior in the presence of ICRF, a 2-D differential equation is being developed which takes into account spatial gradients and mode coupling

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)

The fractional coupled KdV equations: Exact solutions and white noise functional approach

International Nuclear Information System (INIS)

Ghany, Hossam A.; El Bab, A. S. Okb; Zabel, A. M.; Hyder, Abd-Allah

2013-01-01

Variable coefficients and Wick-type stochastic fractional coupled KdV equations are investigated. By using the modified fractional sub-equation method, Hermite transform, and white noise theory the exact travelling wave solutions and white noise functional solutions are obtained, including the generalized exponential, hyperbolic, and trigonometric types. (general)

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)

Novel optical solitary waves and modulation instability analysis for the coupled nonlinear Schrödinger equation in monomode step-index optical fibers

Science.gov (United States)

Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru

2018-01-01

This paper addresses the coupled nonlinear Schrödinger equation (CNLSE) in monomode step-index in optical fibers which describes the nonlinear modulations of two monochromatic waves, whose group velocities are almost equal. A class of dark, bright, dark-bright and dark-singular optical solitary wave solutions of the model are constructed using the complex envelope function ansatz. Singular solitary waves are also retrieved as bye products of the in integration scheme. This naturally lead to some constraint conditions placed on the solitary wave parameters which must hold for the solitary waves to exist. The modulation instability (MI) analysis of the model is studied based on the standard linear-stability analysis. Numerical simulation and physical interpretations of the obtained results are demonstrated. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the CNLSE.

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)

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.

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

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.

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.

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)

Instability of coupled gravity-inertial-Rossby waves on a β-plane in solar system atmospheres

Directory of Open Access Journals (Sweden)

J. F. McKenzie

2009-11-01

Full Text Available This paper provides an analysis of the combined theory of gravity-inertial-Rossby waves on a β-plane in the Boussinesq approximation. The wave equation for the system is fifth order in space and time and demonstrates how gravity-inertial waves on the one hand are coupled to Rossby waves on the other through the combined effects of β, the stratification characterized by the Väisälä-Brunt frequency N, the Coriolis frequency f at a given latitude, and vertical propagation which permits buoyancy modes to interact with westward propagating Rossby waves. The corresponding dispersion equation shows that the frequency of a westward propagating gravity-inertial wave is reduced by the coupling, whereas the frequency of a Rossby wave is increased. If the coupling is sufficiently strong these two modes coalesce giving rise to an instability. The instability condition translates into a curve of critical latitude Θc versus effective equatorial rotational Mach number M, with the region below this curve exhibiting instability. "Supersonic" fast rotators are unstable in a narrow band of latitudes around the equator. For example Θc~12° for Jupiter. On the other hand slow "subsonic" rotators (e.g. Mercury, Venus and the Sun's Corona are unstable at all latitudes except very close to the poles where the β effect vanishes. "Transonic" rotators, such as the Earth and Mars, exhibit instability within latitudes of 34° and 39°, respectively, around the Equator. Similar results pertain to Oceans. In the case of an Earth's Ocean of depth 4km say, purely westward propagating waves are unstable up to 26° about the Equator. The nonlinear evolution of this instability which feeds off rotational energy and gravitational buoyancy may play an important role in atmospheric dynamics.

Propagation of edge waves in a thinly layered laminated medium with stress couples under initial stresses

Directory of Open Access Journals (Sweden)

Pijush Pal Roy

1987-01-01

Full Text Available The propagation of edge waves in a thinly layered laminated medium with stress couples under initial stresses is examined. Based upon an approximate representation of a laminated medium by an equivalent anisotropic continuum with average initial and couple stresses, an explicit form of frequency equation is obtained to derive the phase velocity of edge waves. Edge waves exist under certain conditions. The inclusion of couple stresses increases the velocity of wave propagation. For a specific compression, the presence of couple stresses increases the velocity of wave propagation with the increase of wave number, whereas the reverse is the case when there is no couple stress. Numerical computation is performed with graphical representations. Several special cases are also examined.

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.

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.

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

Theory of Bernstein waves coupling with loop antennas

International Nuclear Information System (INIS)

Brambilla, M.

1987-04-01

We present a fully three-dimensional theory of antenna coupling to Ion Bernstein Waves near the first harmonic of the ion cyclotron resonance in tokamak plasmas. The boundary conditions in vacuum are solved analytically for arbitrary orientation of the antenna and Faraday screen conductors. The wave equations in the plasma, which include Finite Larmor Radius and finite electron inertia effects, cyclotron and harmonic damping by the ions, and Landau and collisional damping by the electrons, are solved numerically using a Finite Elements discretisation with cubic Hermite interpolating functions. Applications to Alcator C give reasonably good agreement between the calculated and measured radiation resistance in the range in which efficient heating is observed; outside this range the calculated resistance is lower than the experimental one. In general, the coupling efficiency is found to be very sensitive to the edge plasma density, good coupling requiring a low density plasma layer in the vicinity of the Faraday screen. Coupling also improves with increasing scrape-off ion temperature, and is appreciably better for antisymmetric than for symmetric toroidal current distributions in the antenna. (orig.)

Exact travelling wave solutions of the Whitham-Broer-Kaup and Broer-Kaup-Kupershmidt equations

International Nuclear Information System (INIS)

Xu Guiqiong; Li Zhibin

2005-01-01

In this paper, an interesting fact is found that the auxiliary equation method is also applicable to a coupled system of two different equations involving both even-order and odd-order partial derivative terms. Furthermore, singular travelling wave solutions can also be obtained by considering other types of exact solutions of auxiliary equation. The Whitham-Broer-Kaup and the (2 + 1)-dimensional Broer-Kaup-Kupershmidt equations are chosen as examples to illustrate the effectiveness of the auxiliary equation method

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

Lamb wave extraction of dispersion curves in micro/nano-plates using couple stress theories

Science.gov (United States)

Ghodrati, Behnam; Yaghootian, Amin; Ghanbar Zadeh, Afshin; Mohammad-Sedighi, Hamid

2018-01-01

In this paper, Lamb wave propagation in a homogeneous and isotropic non-classical micro/nano-plates is investigated. To consider the effect of material microstructure on the wave propagation, three size-dependent models namely indeterminate-, modified- and consistent couple stress theories are used to extract the dispersion equations. In the mentioned theories, a parameter called 'characteristic length' is used to consider the size of material microstructure in the governing equations. To generalize the parametric studies and examine the effect of thickness, propagation wavelength, and characteristic length on the behavior of miniature plate structures, the governing equations are nondimensionalized by defining appropriate dimensionless parameters. Then the dispersion curves for phase and group velocities are plotted in terms of a wide frequency-thickness range to study the lamb waves propagation considering microstructure effects in very high frequencies. According to the illustrated results, it was observed that the couple stress theories in the Cosserat type material predict more rigidity than the classical theory; so that in a plate with constant thickness, by increasing the thickness to characteristic length ratio, the results approach to the classical theory, and by reducing this ratio, wave propagation speed in the plate is significantly increased. In addition, it is demonstrated that for high-frequency Lamb waves, it converges to dispersive Rayleigh wave velocity.

Instability of coupled gravity-inertial-Rossby waves on a β-plane in solar system atmospheres

Directory of Open Access Journals (Sweden)

J. F. McKenzie

2009-11-01

Full Text Available This paper provides an analysis of the combined theory of gravity-inertial-Rossby waves on a β-plane in the Boussinesq approximation. The wave equation for the system is fifth order in space and time and demonstrates how gravity-inertial waves on the one hand are coupled to Rossby waves on the other through the combined effects of β, the stratification characterized by the Väisälä-Brunt frequency N, the Coriolis frequency f at a given latitude, and vertical propagation which permits buoyancy modes to interact with westward propagating Rossby waves. The corresponding dispersion equation shows that the frequency of a westward propagating gravity-inertial wave is reduced by the coupling, whereas the frequency of a Rossby wave is increased. If the coupling is sufficiently strong these two modes coalesce giving rise to an instability. The instability condition translates into a curve of critical latitude Θ_c versus effective equatorial rotational Mach number M, with the region below this curve exhibiting instability. "Supersonic" fast rotators are unstable in a narrow band of latitudes around the equator. For example Θ_c~12° for Jupiter. On the other hand slow "subsonic" rotators (e.g. Mercury, Venus and the Sun's Corona are unstable at all latitudes except very close to the poles where the β effect vanishes. "Transonic" rotators, such as the Earth and Mars, exhibit instability within latitudes of 34° and 39°, respectively, around the Equator. Similar results pertain to Oceans. In the case of an Earth's Ocean of depth 4km say, purely westward propagating waves are unstable up to 26° about the Equator. The nonlinear evolution of this instability which feeds off rotational energy and gravitational buoyancy may play an important role in atmospheric dynamics.

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)

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.

Traveling-wave solutions in continuous chains of unidirectionally coupled oscillators

Science.gov (United States)

Glyzin, S. D.; Kolesov, A. Yu; Rozov, N. Kh

2017-12-01

Proposed is a mathematical model of a continuous annular chain of unidirectionally coupled generators given by certain nonlinear advection-type hyperbolic boundary value problem. Such problems are constructed by a limit transition from annular chains of unidirectionally coupled ordinary differential equations with an unbounded increase in the number of links. It is shown that any preassigned finite number of stable periodic motions of the traveling-wave type can coexist in the model.

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.

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.

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.

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

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)

Test of distorted wave kinematic coupling approximation calculations for knockout reactions

International Nuclear Information System (INIS)

Jain, A.K.

1990-01-01

A test has been devised to check the validity of conventional distorted-wave impulse approximation (DWIA) treatment of knockout reactions. The conventional DWIA formalism separates the three-body final state Schroedinger equation for a knockout reaction into two two-body Schroedinger equations by assuming an asymptotic constant value for the three-body coupling term commonly known as the kinematic coupling approximation (KCA). In the test case, which consists of an extreme asymmetric situation where one of the distorting optical potentials is assumed to vanish, the three-body final state Schroedinger equation can be solved exactly as a product of two two-body solutions using one particular set of relative coordinates. Large influence of the three-body coupling term is seen in the comparison of the exact and KCA results for (α,2α) and (p,pα) knockout reactions when the distorting optical potentials are weakly absorbing

A Calderón multiplicative preconditioner for coupled surface-volume electric field integral equations

KAUST Repository

Bagci, Hakan; Andriulli, Francesco P.; Cools, Kristof; Olyslager, Femke; Michielssen, Eric

2010-01-01

A well-conditioned coupled set of surface (S) and volume (V) electric field integral equations (S-EFIE and V-EFIE) for analyzing wave interactions with densely discretized composite structures is presented. Whereas the V-EFIE operator is well

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

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.

Toward nonlinear magnonics: Intensity-dependent spin-wave switching in insulating side-coupled magnetic stripes

Science.gov (United States)

Sadovnikov, A. V.; Odintsov, S. A.; Beginin, E. N.; Sheshukova, S. E.; Sharaevskii, Yu. P.; Nikitov, S. A.

2017-10-01

We demonstrate that the nonlinear spin-wave transport in two laterally parallel magnetic stripes exhibit the intensity-dependent power exchange between the adjacent spin-wave channels. By the means of Brillouin light scattering technique, we investigate collective nonlinear spin-wave dynamics in the presence of magnetodipolar coupling. The nonlinear intensity-dependent effect reveals itself in the spin-wave mode transformation and differential nonlinear spin-wave phase shift in each adjacent magnetic stripe. The proposed analytical theory, based on the coupled Ginzburg-Landau equations, predicts the geometry design involving the reduction of power requirement to the all-magnonic switching. A very good agreement between calculation and experiment was found. In addition, a micromagnetic and finite-element approach has been independently used to study the nonlinear behavior of spin waves in adjacent stripes and the nonlinear transformation of spatial profiles of spin-wave modes. Our results show that the proposed spin-wave coupling mechanism provides the basis for nonlinear magnonic circuits and opens the perspectives for all-magnonic computing architecture.

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.

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.

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...

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

On the stability, the periodic solutions and the resolution of certain types of non linear equations, and of non linearly coupled systems of these equations, appearing in betatronic oscillations

International Nuclear Information System (INIS)

Valat, J.

1960-12-01

Universal stability diagrams have been calculated and experimentally checked for Hill-Meissner type equations with square-wave coefficients. The study of these equations in the phase-plane has then made it possible to extend the periodic solution calculations to the case of non-linear differential equations with periodic square-wave coefficients. This theory has been checked experimentally. For non-linear coupled systems with constant coefficients, a search was first made for solutions giving an algebraic motion. The elliptical and Fuchs's functions solve such motions. The study of non-algebraic motions is more delicate, apart from the study of nonlinear Lissajous's motions. A functional analysis shows that it is possible however in certain cases to decouple the system and to find general solutions. For non-linear coupled systems with periodic square-wave coefficients it is then possible to calculate the conditions leading to periodic solutions, if the two non-linear associated systems with constant coefficients fall into one of the categories of the above paragraph. (author) [fr

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

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.

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.

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.

On Rayleigh waves in a thinly layered laminated thermoelastic medium with stress couples under initial stresses

Directory of Open Access Journals (Sweden)

Pijush Pal Roy

1988-01-01

Full Text Available A study is made of the propagation of Rayleigh waves in a thinly layered laminated thermoelastic medium under deviatoric, hydrostatic, and couple stresses. The frequency equation of the Rayleigh waves is obtained. The phase velocity of the Rayleigh waves depends on the initial stress, deviatoric stress, and the couple stress. The laminated medium is first replaced by an equivalent anisotropic thermoelastic continuum. The corresponding thermoelastic coefficients (after deformation are derived in terms of initially isotropic thermoelastic coefficients (before deformation of individual layers. Several particular cases are discussed for the determination of the displacement fields with or without the effect of the couple stress.

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

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

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

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.

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

Localized excitations in a nonlinearly coupled magnetic drift wave-zonal flow system

International Nuclear Information System (INIS)

Shukla, Nitin; Shukla, P.K.

2010-01-01

We consider the amplitude modulation of the magnetic drift wave (MDW) by zonal flows (ZFs) in a nonuniform magnetoplasma. For this purpose, we use the two-fluid model to derive a nonlinear Schroedinger equation for the amplitude modulated MDWs in the presence of the ZF potential, and an evolution equation for the ZF potential which is reinforced by the nonlinear Lorentz force of the MDWs. Our nonlinearly coupled MDW-ZFs system of equations admits stationary solutions in the form of a localized MDW envelope and a shock-like ZF potential profile.

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.

Coupling Integrable Couplings of an Equation Hierarchy

International Nuclear Information System (INIS)

Wang Hui; Xia Tie-Cheng

2013-01-01

Based on a kind of Lie algebra G proposed by Zhang, one isospectral problem is designed. Under the framework of zero curvature equation, a new kind of integrable coupling of an equation hierarchy is generated using the methods proposed by Ma and Gao. With the help of variational identity, we get the Hamiltonian structure of the hierarchy. (general)

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.

Self-consistent calculation of the coupling constant in the Gross-Pitaevskii equation

International Nuclear Information System (INIS)

Cherny, A.Yu.; Brand, J.

2004-01-01

A method is proposed for a self-consistent evaluation of the coupling constant in the Gross-Pitaevskii equation without involving a pseudopotential replacement. A renormalization of the coupling constant occurs due to medium effects and the trapping potential, e.g., in quasi-1D or quasi-2D systems. It is shown that a simplified version of the Hartree-Fock-Bogoliubov approximation leads to a variational problem for both the condensate and a two-body wave function describing the behavior of a pair of bosons in the Bose-Einstein condensate. The resulting coupled equations are free of unphysical divergences. Particular cases of this scheme that admit analytical estimations are considered and compared to the literature. In addition to the well-known cases of low-dimensional trapping, crossover regimes can be studied. The values of the kinetic, interaction, external, and release energies in low dimensions are also evaluated and contributions due to short-range correlations are found to be substantial

Solving Nonlinear Coupled Differential Equations

Science.gov (United States)

Mitchell, L.; David, J.

1986-01-01

Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.

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.)

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)

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

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

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

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

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).

Velocity-space diffusion due to resonant wave-wave scattering of electromagnetic and electrostatic waves in a plasma

International Nuclear Information System (INIS)

Sugaya, Reija

1991-01-01

The velocity-space diffusion equation describing distortion of the velocity distribution function due to resonant wave-wave scattering of electromagnetic and electrostatic waves in an unmagnetized plasma is derived from the Vlasov-Maxwell equations by perturbation theory. The conservation laws for total energy and momentum densities of waves and particles are verified, and the time evolutions of the energy and momentum densities of particles are given in terms of the nonlinear wave-wave coupling coefficient in the kinetic wave equation. (author)

Hamiltonian approach to the derivation of evolution equations for wave trains in weakly unstable media

Directory of Open Access Journals (Sweden)

N. N. Romanova

1998-01-01

Full Text Available The dynamics of weakly nonlinear wave trains in unstable media is studied. This dynamics is investigated in the framework of a broad class of dynamical systems having a Hamiltonian structure. Two different types of instability are considered. The first one is the instability in a weakly supercritical media. The simplest example of instability of this type is the Kelvin-Helmholtz instability. The second one is the instability due to a weak linear coupling of modes of different nature. The simplest example of a geophysical system where the instability of this and only of this type takes place is the three-layer model of a stratified shear flow with a continuous velocity profile. For both types of instability we obtain nonlinear evolution equations describing the dynamics of wave trains having an unstable spectral interval of wavenumbers. The transformation to appropriate canonical variables turns out to be different for each case, and equations we obtained are different for the two types of instability we considered. Also obtained are evolution equations governing the dynamics of wave trains in weakly subcritical media and in media where modes are coupled in a stable way. Presented results do not depend on a specific physical nature of a medium and refer to a broad class of dynamical systems having the Hamiltonian structure of a special form.

Theoretical and experimental study of the hybrid wave coupling in Tore Supra and Jet by multijunction antennas

International Nuclear Information System (INIS)

Litaudon, X.

1990-06-01

The hybrid or slow electron plasma waves propagation and coupling are investigated in a toroidal magnetic confinement configuration such as found in Tokamaks. The main characteristics of the antenna, formed of several waveguides displaced in the toroidal direction, are studied. The equations of the hybrid waves linear propagation are solved for a plane geometrical configuration and in an inhomogeneous plasma. The optimization of the hybrid wave couplers of Tore Supra and Jet is carried out by means of the SWAN code. The results of the experiments performed on Tore Supra are analyzed. The investigation shows that the wave coupling depends on the edge plasma properties [fr

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

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.

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....

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.

Dynamics of wide and snake-like pulses in coupled Schrödinger equations with full-modulated nonlinearities

Energy Technology Data Exchange (ETDEWEB)

Yomba, Emmanuel, E-mail: emmanuel.yomba@csun.edu; Zakeri, Gholam-Ali, E-mail: ali.zakeri@csun.edu

2016-02-05

We investigate the existence of various solitary wave solutions in coupled Schrödinger equations with specific cubic and quintic nonlinearities. This system arises in wave propagation in fiber optics with focusing and defocusing with modulated nonlinearities. We obtain front–front, bright–bright, dark–dark, and dark–bright like solitons using a direct approach, and then, by reducing the system of equations to a single auxiliary equation of a Duffing-type ordinary differential equation, we provide a large class of Jacobi-elliptic solutions. These solutions are presented in the exact form and analyzed. We find a class of wide localized and snake-like (in both space and time) vector solitons. One of the novel aspects of this study is that we have shown that the qualitative behavior of the solutions is independent of the choice of similarity variables. Numerical results show that the solutions of the above system are stable with up to 10% white noises. - Highlights: • Dynamics of wide and snake-like pulses is analyzed for coupled Schrödinger equations. • Qualitative appearance of solutions is analyzed using various similarity variables. • Effect of change in parameter-values on dynamics of the solutions is investigated. • Vectors front–front, bright–bright, dark–dark and dark–bright solitons are obtained.

Propagation of SH waves in a piezoelectric/piezomagnetic plate: Effects of interfacial imperfection couplings and the related physical mechanisms

Energy Technology Data Exchange (ETDEWEB)

Wei, Hong-Xing [Beijing Advanced Innovation Center for Imaging Technology, Capital Normal University, Beijing 100048 (China); Li, Yong-Dong, E-mail: LYDbeijing@163.com [Beijing Advanced Innovation Center for Imaging Technology, Capital Normal University, Beijing 100048 (China); Department of Mechanical Engineering, Academy of Armored Force Engineering, Beijing 100072 (China); Xiong, Tao [Department of Mechanical Engineering, Academy of Armored Force Engineering, Beijing 100072 (China); Guan, Yong [Beijing Advanced Innovation Center for Imaging Technology, Capital Normal University, Beijing 100048 (China)

2016-09-07

The problem of dispersive SH wave in a piezoelectric/piezomagnetic plate that contains an imperfect interface is considered in the present work. An imperfection coupling model is adopted to describe the magnetic, electric and mechanical imperfections on the interface. A transcendental dispersion equation is derived and numerically solved to get the phase velocity. The validity of the numerical procedure is verified in a degenerated case. The effects of the coupled interfacial imperfections on the dispersion behavior of SH waves are discussed in detail and the related underlying physical mechanisms are explained. - Highlights: • SH-wave is investigated in a multiferroic plate with coupled interfacial imperfections. • SH-wave is affected by both interfacial imperfections and their inter-couplings. • Physical mechanisms of the effects are explained via energy transformations.

Propagation of SH waves in a piezoelectric/piezomagnetic plate: Effects of interfacial imperfection couplings and the related physical mechanisms

International Nuclear Information System (INIS)

Wei, Hong-Xing; Li, Yong-Dong; Xiong, Tao; Guan, Yong

2016-01-01

The problem of dispersive SH wave in a piezoelectric/piezomagnetic plate that contains an imperfect interface is considered in the present work. An imperfection coupling model is adopted to describe the magnetic, electric and mechanical imperfections on the interface. A transcendental dispersion equation is derived and numerically solved to get the phase velocity. The validity of the numerical procedure is verified in a degenerated case. The effects of the coupled interfacial imperfections on the dispersion behavior of SH waves are discussed in detail and the related underlying physical mechanisms are explained. - Highlights: • SH-wave is investigated in a multiferroic plate with coupled interfacial imperfections. • SH-wave is affected by both interfacial imperfections and their inter-couplings. • Physical mechanisms of the effects are explained via energy transformations.

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)

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

Numerical study of laser-induced blast wave coupled with unsteady ionization processes

International Nuclear Information System (INIS)

Ogino, Y; Ohnishi, N; Sawada, K

2008-01-01

We present the results of the numerical simulation of laser-induced blast wave coupled with rate equations to clarify the unsteady property of ionization processes during pulse heating. From comparison with quasi-steady computations, the plasma region expands more widely, which is sustained by the inverse-bremsstrahlung since an ionization equilibrium does not establish at the front of the plasma region. The delayed relaxation leads to the rapid expansion of the driving plasma and enhances the energy conversion efficiency from a pulse heating laser to the blast wave

Integrable coupling system of fractional soliton equation hierarchy

Energy Technology Data Exchange (ETDEWEB)

Yu Fajun, E-mail: yfajun@163.co [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China)

2009-10-05

In this Letter, we consider the derivatives and integrals of fractional order and present a class of the integrable coupling system of the fractional order soliton equations. The fractional order coupled Boussinesq and KdV equations are the special cases of this class. Furthermore, the fractional AKNS soliton equation hierarchy is obtained.

Two-body Dirac equation and its wave function at the origin

International Nuclear Information System (INIS)

Ito, Hitoshi

1998-01-01

We propose a relativistic bound state equation for the Dirac particles interacting through an Abelian gauge field. It reduces to the (one body) Dirac equation in the infinite limit of one of the masses and is invariant under the PCT transformation. This invariance is a consequence of a modification of the Stueckelberg-Feynman boundary condition for propagation of the negative-energy two-body states, by which the some effect of the crossed diagram is taken in the lowest ladder equation. We can correct back the modification in perturbative calculations of the weak-coupling theory by adding a counter correction term in the interaction kernel. The equation can be used for the phenomenology of the heavy flavored mesons. We get good behavior of the wave function at the origin (WFO), with which the annihilation amplitude of the pseudoscalar meson becomes finite. Some comments are mentioned for the application in the heavy quark effective theory. The talk was based on a preprint

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

EXACT TRAVELLING WAVE SOLUTIONS TO BBM EQUATION

Institute of Scientific and Technical Information of China (English)

无

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.

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

Charging-delay effect on longitudinal dust acoustic shock wave in strongly coupled dusty plasma

International Nuclear Information System (INIS)

Ghosh, Samiran; Gupta, M.R.

2005-01-01

Taking into account the charging-delay effect, the nonlinear propagation characteristics of longitudinal dust acoustic wave in strongly coupled collisional dusty plasma described by generalized hydrodynamic model have been investigated. In the 'hydrodynamic limit', a Korteweg-de Vries Burger (KdVB) equation with a damping term arising due to dust-neutral collision is derived in which the Burger term is proportional to the dissipation due to dust viscosity through dust-dust correlation and charging-delay-induced anomalous dissipation. On the other hand, in the 'kinetic limit', a KdVB equation with a damping term and a nonlocal nonlinear forcing term arising due to memory-dependent strong correlation effect of dust fluid is derived in which the Burger term depends only on the charging-delay-induced dissipation. Numerical solution of integrodifferential equations reveals that (i) dissipation due to dust viscosity and principally due to charging delay causes excitation of the longitudinal dust acoustic shock wave in strongly coupled dusty plasma and (ii) dust-neutral collision does not appear to play any direct role in shock formation. The condition for the generation of shock is also discussed briefly

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.

Reciprocal link for a coupled Camassa–Holm type equation

International Nuclear Information System (INIS)

Li, Nianhua; Zhang, Jinshun; Wu, Lihua

2016-01-01

Highlights: • We construct a reciprocal transformation for a coupled Camassa–Holm type equation proposed by Geng and Xue. • The transformed coupled Camassa–Holm type system is a reduction of the first negative flow in a modified Drinfeld–Sokolov III hierarchy. • The Lax pair and bi-Hamiltonian structure behaviors of the coupled Camassa–Holm type equation under the reciprocal transformation are analyzed. - Abstract: A coupled Camassa–Holm type equation is linked to the first negative flow in a modified Drinfeld–Sokolov III hierarchy by a transformation of reciprocal type. Meanwhile the Lax pair and bi-Hamiltonian structure behaviors of this coupled Camassa–Holm type equation under the reciprocal transformation are analyzed.

Introducing time-dependent molecular fields: a new derivation of the wave equations

Science.gov (United States)

Baer, Michael

2018-02-01

This article is part of a series of articles trying to establish the concept molecular field. The theory that induced us to introduce this novel concept is based on the Born-Huang expansion as applied to the Schroedinger equation that describes the interaction of a molecular system with an external electric field. Assuming the molecular system is made up of two coupled adiabatic states the theory leads from a single spatial curl equation, two space-time curl equations and one single space-time divergent equation to a pair of decoupled wave equations usually encountered within the theory of fields. In the present study, just like in the previous study [see Baer et al., Mol. Phys. 114, 227 (2016)] the wave equations are derived for an electric field having two features: (a) its intensity is high enough; (b) its duration is short enough. Although not all the findings are new the derivation, in the present case, is new, straightforward, fluent and much friendlier as compared to the previous one and therefore should be presented again. For this situation the study reveals that the just described interaction creates two fields that coexist within a molecule: one is a novel vectorial field formed via the interaction of the electric field with the Born-Huang non-adiabatic coupling terms (NACTs) and the other is an ordinary, scalar, electric field essentially identical to the original electric field. Section 4 devoted to the visualization of the outcomes via two intersecting Jahn-Teller cones which contain NACTs that become singular at the intersection point of these cones. Finally, the fact that eventually we are facing a kind of a cosmic situation may bring us to speculate that singular NACTs are a result of cosmic phenomena. Thus, if indeed this singularity is somehow connected to reality then, like other singularities in physics, it is formed at (or immediately after) the Big Bang and consequently, guarantees the formation of molecules.

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.

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.

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).

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].

Minimally coupled N-particle scattering integral equations

International Nuclear Information System (INIS)

Kowalski, K.L.

1977-01-01

A concise formalism is developed which permits the efficient representation and generalization of several known techniques for deriving connected-kernel N-particle scattering integral equations. The methods of Kouri, Levin, and Tobocman and Bencze and Redish which lead to minimally coupled integral equations are of special interest. The introduction of channel coupling arrays is characterized in a general manner and the common base of this technique and that of the so-called channel coupling scheme is clarified. It is found that in the Bencze-Redish formalism a particular coupling array has a crucial function but one different from that of the arrays employed by Kouri, Levin, and Tobocman. The apparent dependence of the proof of the minimality of the Bencze-Redish integral equations upon the form of the inhomogeneous term in these equations is eliminated. This is achieved by an investigation of the full (nonminimal) Bencze-Redish kernel. It is shown that the second power of this operator is connected, a result which is needed for the full applicability of the Bencze-Redish formalism. This is used to establish the relationship between the existence of solutions to the homogeneous form of the minimal equations and eigenvalues of the full Bencze-Redish kernel

Hydromagnetic wave coupling in the magnetosphere

International Nuclear Information System (INIS)

Lee, D.

1990-01-01

The hydromagnetic wave phenomena in the magnetosphere has been an area of space physics and plasma physics where theory has been successful in explaining many features in satellite experiments and ground-based observations. Magnetohydrodynamic (MHD) waves, which are composed of transverse Alven waves and compressional waves, are usually coupled in space due to an inhomogeneous plasma density and curved magnetic field lines. In addition to these effects, hot temperature plasmas invoke various ultra low frequency (ULF) wave phenomena via macroscopic wave instabilities or wave particle resonant interactions. These properties of the coupling between the two different MHD waves were analytically and numerically studied in a simplified model such as the box model with straight field lines. However, the real magnetosphere is rather close to a dipole field, even though the night side of the magnetosphere is significantly distorted from dipole geometry. The curvature of field lines plays an important role in understanding hydromagnetic wave coupling in the magnetosphere since the MHD wave propagation depends strongly on the curved magnetic fields. The study of the hydromagnetic wave properties on an inhomogeneous and curved magnetic field system by considering realistic geometry is emphasized. Most of the current theories are reviewed and a number of observations are introduced according to the wave excitation mechanism. Studies are also performed with the development of numerical models such as the two and three dimensional MHD dipole models. An attempt is made to understand and classify the hydromagnetic wave behavior in inhomogeneous and hot plasmas with respect to the energy sources and their frequency band in the magnetosphere. Therefore, various excitation mechanisms for hydromagnetic waves are examined to compare analytical and numerical results with the observations

Traveling Wave-Guide Channels of a New Coupled Integrable Dispersionless System

International Nuclear Information System (INIS)

Souleymanou, Abbagari; Kuetche, Victor K.; Bouetou, Thomas B.; Kofane, Timoleon C.

2012-01-01

In the wake of the recent investigation of new coupled integrable dispersionless equations by means of the Darboux transformation [Zhaqilao, et al., Chin. Phys. B 18 (2009) 1780], we carry out the initial value analysis of the previous system using the fourth-order Runge-Kutta's computational scheme. As a result, while depicting its phase portraits accordingly, we show that the above dispersionless system actually supports two kinds of solutions amongst which the localized traveling wave-guide channels. In addition, paying particular interests to such localized structures, we construct the bilinear transformation of the current system from which scattering amongst the above waves can be deeply studied. (general)

Exploring AdS waves via nonminimal coupling

International Nuclear Information System (INIS)

Ayon-Beato, Eloy; Hassaiene, Mokhtar

2006-01-01

We consider nonminimally coupled scalar fields to explore the Siklos spacetimes in three dimensions. Their interpretation as exact gravitational waves propagating on AdS space restrict the source to behave as a pure radiation field. We show that the related pure radiation constraints single out a unique self-interaction potential depending on one coupling constant. For a vanishing coupling constant, this potential reduces to a mass term with a mass fixed in terms of the nonminimal-coupling parameter. This mass dependence allows the existence of several free cases including massless and tachyonic sources. There even exists a particular value of the nonminimal-coupling parameter for which the corresponding mass exactly compensates the contribution generated by the negative scalar curvature, producing a genuinely massless field in this curved background. The self-interacting case is studied in detail for the conformal coupling. The resulting gravitational wave is formed by the superposition of the free and the self-interaction contributions, except for a critical value of the coupling constant where a nonperturbative effect relating the strong and weak regimes of the source appears. We establish a correspondence between the scalar source supporting an AdS wave and a pp wave by showing that their respective pure radiation constraints are conformally related, while their involved backgrounds are not. Finally, we consider the AdS waves for topologically massive gravity and its limit to conformal gravity

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.

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.

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.

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

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.

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

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.

Non-Linear Excitation of Ion Acoustic Waves

DEFF Research Database (Denmark)

Michelsen, Poul; Hirsfield, J. L.

1974-01-01

The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation.......The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation....

Variational iteration method for solving coupled-KdV equations

International Nuclear Information System (INIS)

Assas, Laila M.B.

2008-01-01

In this paper, the He's variational iteration method is applied to solve the non-linear coupled-KdV equations. This method is based on the use of Lagrange multipliers for identification of optimal value of a parameter in a functional. This technique provides a sequence of functions which converge to the exact solution of the coupled-KdV equations. This procedure is a powerful tool for solving coupled-KdV equations

Two-wave mixing in a broad-area semiconductor amplifier

DEFF Research Database (Denmark)

Chi, M.; Jensen, S.B.; Huignard, J.P.

2006-01-01

The two-wave mixing in the broad-area semiconductor amplifier was investigated, both theoretically and experimentally. In detail we investigated how the optical gain is affected by the presence of the two-wave mixing interference grating. In the experimental setup we are able to turn on and off...... the interference pattern in the semiconductor amplifier. This arrangement allows us to determine the two-wave mixing gain. The coupled-wave equations of two-wave mixing were derived based on the Maxwell’s wave equation and rate equation of the carrier density. The analytical solutions of the coupled-wave equations...

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.

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)

Nonlinear spin wave coupling in adjacent magnonic crystals

Energy Technology Data Exchange (ETDEWEB)

Sadovnikov, A. V., E-mail: sadovnikovav@gmail.com; Nikitov, S. A. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation); Kotel' nikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, Moscow 125009 (Russian Federation); Beginin, E. N.; Morozova, M. A.; Sharaevskii, Yu. P.; Grishin, S. V.; Sheshukova, S. E. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation)

2016-07-25

We have experimentally studied the coupling of spin waves in the adjacent magnonic crystals. Space- and time-resolved Brillouin light-scattering spectroscopy is used to demonstrate the frequency and intensity dependent spin-wave energy exchange between the side-coupled magnonic crystals. The experiments and the numerical simulation of spin wave propagation in the coupled periodic structures show that the nonlinear phase shift of spin wave in the adjacent magnonic crystals leads to the nonlinear switching regime at the frequencies near the forbidden magnonic gap. The proposed side-coupled magnonic crystals represent a significant advance towards the all-magnonic signal processing in the integrated magnonic circuits.

Nonlinear spin wave coupling in adjacent magnonic crystals

International Nuclear Information System (INIS)

Sadovnikov, A. V.; Nikitov, S. A.; Beginin, E. N.; Morozova, M. A.; Sharaevskii, Yu. P.; Grishin, S. V.; Sheshukova, S. E.

2016-01-01

We have experimentally studied the coupling of spin waves in the adjacent magnonic crystals. Space- and time-resolved Brillouin light-scattering spectroscopy is used to demonstrate the frequency and intensity dependent spin-wave energy exchange between the side-coupled magnonic crystals. The experiments and the numerical simulation of spin wave propagation in the coupled periodic structures show that the nonlinear phase shift of spin wave in the adjacent magnonic crystals leads to the nonlinear switching regime at the frequencies near the forbidden magnonic gap. The proposed side-coupled magnonic crystals represent a significant advance towards the all-magnonic signal processing in the integrated magnonic circuits.

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

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

Energy-flux characterization of conical and space-time coupled wave packets

International Nuclear Information System (INIS)

Lotti, A.; Couairon, A.; Faccio, D.; Trapani, P. Di

2010-01-01

We introduce the concept of energy density flux as a characterization tool for the propagation of ultrashort laser pulses with spatiotemporal coupling. In contrast with calculations for the Poynting vector, those for energy density flux are derived in the local frame moving at the velocity of the envelope of the wave packet under examination and do not need knowledge of the magnetic field. We show that the energy flux defined from a paraxial propagation equation follows specific geometrical connections with the phase front of the optical wave packet, which demonstrates that the knowledge of the phase fronts amounts to the measurement of the energy flux. We perform a detailed numerical study of the energy density flux in the particular case of conical waves, with special attention paid to stationary-envelope conical waves (X or O waves). A full characterization of linear conical waves is given in terms of their energy flux. We extend the definition of this concept to the case of nonlinear propagation in Kerr media with nonlinear losses.

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.

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

Flashing coupled density wave oscillation

International Nuclear Information System (INIS)

Jiang Shengyao; Wu Xinxin; Zhang Youjie

1997-07-01

The experiment was performed on the test loop (HRTL-5), which simulates the geometry and system design of the 5 MW reactor. The phenomenon and mechanism of different kinds of two-phase flow instabilities, namely geyser instability, flashing instability and flashing coupled density wave instability are described. The especially interpreted flashing coupled density wave instability has never been studied well, it is analyzed by using a one-dimensional non-thermo equilibrium two-phase flow drift model computer code. Calculations are in good agreement with the experiment results. (5 refs.,5 figs., 1 tab.)

Coupled Higgs field equation and Hamiltonian amplitude equation ...

Indian Academy of Sciences (India)

Home; Journals; Pramana – Journal of Physics; Volume 79; Issue 1. Coupled Higgs field equation and ... School of Mathematics and Computer Applications, Thapar University, Patiala 147 004, India; Department of Mathematics, Jaypee University of Information Technology, Waknaghat, Distt. Solan 173 234, India ...

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.

The effect of Coriolis-Stokes forcing on upper ocean circulation in a two-way coupled wave-current model

Institute of Scientific and Technical Information of China (English)

DENG Zeng'an; XIE Li'an; HAN Guijun; ZHANG Xuefeng; WU Kejian

2012-01-01

We investigated the Stokes drift-driven ocean currents and Stokes drift-induced wind energy input into the upper ocean using a two-way coupled wave-current modeling system that consists of the Princeton Ocean Model generalized coordinate system (POMgcs),Simulating WAves Nearshore (SWAN) wave model,and the Model Coupling Toolkit (MCT).The Coriolis-Stokes forcing (CSF) computed using the wave parameters from SWAN was incorporated with the momentum equation of POMgcs as the core coupling process.Experimental results in an idealized setting show that under the steady state,the scale of the speed of CSF-driven current was 0.001 m/s and the maximum reached 0.02 rn/s.The Stokes drift-induced energy rate input into the model ocean was estimated to be 28.5 GW,taking 14％ of the direct wind energy rate input.Considering the Stokes drift effects,the total mechanical energy rate input was increased by approximately 14％,which highlights the importance of CSF in modulating the upper ocean circulation.The actual run conducted in Taiwan Adjacent Sea (TAS) shows that:1) CSF-based wave-current coupling has an impact on ocean surface currents,which is related to the activities of monsoon winds; 2) wave-current coupling plays a significant role in a place where strong eddies present and tends to intensify the eddy's vorticity; 3) wave-current coupling affects the volume transport of the Taiwan Strait (TS) throughflow in a nontrivial degree,3.75％ on average.

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....

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.)

Hybridizable discontinuous Galerkin method for the 2-D frequency-domain elastic wave equations

Science.gov (United States)

Bonnasse-Gahot, Marie; Calandra, Henri; Diaz, Julien; Lanteri, Stéphane

2018-04-01

Discontinuous Galerkin (DG) methods are nowadays actively studied and increasingly exploited for the simulation of large-scale time-domain (i.e. unsteady) seismic wave propagation problems. Although theoretically applicable to frequency-domain problems as well, their use in this context has been hampered by the potentially large number of coupled unknowns they incur, especially in the 3-D case, as compared to classical continuous finite element methods. In this paper, we address this issue in the framework of the so-called hybridizable discontinuous Galerkin (HDG) formulations. As a first step, we study an HDG method for the resolution of the frequency-domain elastic wave equations in the 2-D case. We describe the weak formulation of the method and provide some implementation details. The proposed HDG method is assessed numerically including a comparison with a classical upwind flux-based DG method, showing better overall computational efficiency as a result of the drastic reduction of the number of globally coupled unknowns in the resulting discrete HDG system.

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.

Instability of nonplanar modulated dust acoustic wave packets in a strongly coupled nonthermal dusty plasma

Energy Technology Data Exchange (ETDEWEB)

El-Labany, S. K., E-mail: skellabany@hotmail.com; Zedan, N. A., E-mail: nesreenplasma@yahoo.com [Department of Physics, Faculty of Science, Damietta University, New Damietta, P.O. 34517 (Egypt); El-Taibany, W. F., E-mail: eltaibany@hotmail.com, E-mail: eltaibany@du.edu.eg [Department of Physics, Faculty of Science, Damietta University, New Damietta, P.O. 34517 (Egypt); Department of Physics, College of Science for Girls in Abha, King Khalid University, P.O. 960 Abha (Saudi Arabia)

2015-07-15

Cylindrical and spherical amplitude modulations of dust acoustic (DA) solitary wave envelopes in a strongly coupled dusty plasma containing nonthermal distributed ions are studied. Employing a reductive perturbation technique, a modified nonlinear Schrödinger equation including the geometrical effect is derived. The influences of nonthermal ions, polarization force, and the geometries on the modulational instability conditions are analyzed and the possible rogue wave structures are discussed in detail. It is found that the spherical DA waves are more structurally stable to perturbations than the cylindrical ones. Possible applications of these theoretical findings are briefly discussed.

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.

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)

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.

Dirac equation in 2-dimensional curved spacetime, particle creation, and coupled waveguide arrays

Energy Technology Data Exchange (ETDEWEB)

Koke, Christian, E-mail: christian.koke@stud.uni-heidelberg.de [Institut für theoretische Physik, Philosophenweg 16, D-69120 Heidelberg (Germany); Noh, Changsuk, E-mail: changsuk@kias.re.kr [Korea Institute for Advanced Study, 85 Hoegiro, Seoul 130-722 (Korea, Republic of); Angelakis, Dimitris G., E-mail: dimitris.angelakis@gmail.com [Centre for Quantum Technologies, National University of Singapore, 2 Science Drive 3, 117542 (Singapore); School of Electronic and Computer Engineering, Technical University of Crete, Chania, Crete, 73100 (Greece)

2016-11-15

When quantum fields are coupled to gravitational fields, spontaneous particle creation may occur similarly to when they are coupled to external electromagnetic fields. A gravitational field can be incorporated as a background spacetime if the back-action of matter on the field can be neglected, resulting in modifications of the Dirac or Klein–Gordon equations for elementary fermions and bosons respectively. The semi-classical description predicts particle creation in many situations, including the expanding-universe scenario, near the event horizon of a black hole (the Hawking effect), and an accelerating observer in flat spacetime (the Unruh effect). In this work, we give a pedagogical introduction to the Dirac equation in a general 2D spacetime and show examples of spinor wave packet dynamics in flat and curved background spacetimes. In particular, we cover the phenomenon of particle creation in a time-dependent metric. Photonic analogs of these effects are then proposed, where classical light propagating in an array of coupled waveguides provides a visualisation of the Dirac spinor propagating in a curved 2D spacetime background. The extent to which such a single-particle description can be said to mimic particle creation is discussed.

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...

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

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.

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 ...

Numerical resolution of Navier-Stokes equations coupled to the heat equation

International Nuclear Information System (INIS)

Zenouda, Jean-Claude

1970-08-01

The author proves a uniqueness theorem for the time dependent Navier-Stokes equations coupled with heat flow in the two-dimensional case. He studies stability and convergence of several finite - difference schemes to solve these equations. Numerical experiments are done in the case of a square domain. (author) [fr

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.

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.

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.)

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

Reverse-time Migration in Tilted Transversely Isotropic Media with Decoupled Equations

KAUST Repository

Zhan, Ge

2012-12-01

Conventional modeling and migration for tilted transversely isotropic (TTI) media may suffer from numerical instabilities and shear wave artifacts due to the coupling of the P-wave and SV-wave modes in the TTI coupled equations. Starting with the separated P- and SV-phase velocity expressions for vertical transversely isotropic (VTI) media, I extend these decoupled equations for modeling and reverse-time migration (RTM) in acoustic TTI media. Compared with the TTI coupled equations published in the geophysical literature, the new TTI decoupled equations provide a more stable solution due to the complete separation of the P-wave and SV-wave modes. The pseudospectral (PS) method is the most convenient method to implement these equations due to the form of wavenumber expressions and has the added benefit of being highly accurate and thus avoiding numerical dispersion. The rapid expansion method (REM) in time is employed to produce a broad band numerically stable time evolution of the wavefields. Synthetic results validate the proposed TTI decoupled equations and show that modeling and RTM in TTI media with the decoupled P-wave equation remain numerically stable even for models with strong anisotropy and sharp contrasts. The most desirable feature of the TTI decoupled P-wave equation is that it is absolutely free of shear-wave artifacts 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 extrapolation at each time step, the computational cost is also high, and thereby hampers its prevalence. I hereby propose to use a hybrid pseudospectral and finite-difference (FD) scheme to solve the TTI decoupled 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

Soliton solutions of coupled nonlinear Klein-Gordon equations

International Nuclear Information System (INIS)

Alagesan, T.; Chung, Y.; Nakkeeran, K.

2004-01-01

The coupled nonlinear Klein-Gordon equations are analyzed for their integrability properties in a systematic manner through Painleve test. From the Painleve test, by truncating the Laurent series at the constant level term, the Hirota bilinear form is identified, from which one-soliton solutions are derived. Then, the results are generalized to the two, three and N-coupled Klein-Gordon equations

Vibrations and waves

CERN Document Server

Kaliski, S

2013-01-01

This book gives a comprehensive overview of wave phenomena in different media with interacting mechanical, electromagnetic and other fields. Equations describing wave propagation in linear and non-linear elastic media are followed by equations of rheological models, models with internal rotational degrees of freedom and non-local interactions. Equations for coupled fields: thermal, elastic, electromagnetic, piezoelectric, and magneto-spin with adequate boundary conditions are also included. Together with its companion volume Vibrations and Waves. Part A: Vibrations this work provides a wealth

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

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

SBP-SAT finite difference discretization of acoustic wave equations on staggered block-wise uniform grids

KAUST Repository

Gao, Longfei

2018-02-16

We consider the numerical simulation of the acoustic wave equations arising from seismic applications, for which staggered grid finite difference methods are popular choices due to their simplicity and efficiency. We relax the uniform grid restriction on finite difference methods and allow the grids to be block-wise uniform with nonconforming interfaces. In doing so, variations in the wave speeds of the subterranean media can be accounted for more efficiently. Staggered grid finite difference operators satisfying the summation-by-parts (SBP) property are devised to approximate the spatial derivatives appearing in the acoustic wave equation. These operators are applied within each block independently. The coupling between blocks is achieved through simultaneous approximation terms (SATs), which impose the interface condition weakly, i.e., by penalty. Ratio of the grid spacing of neighboring blocks is allowed to be rational number, for which specially designed interpolation formulas are presented. These interpolation formulas constitute key pieces of the simultaneous approximation terms. The overall discretization is shown to be energy-conserving and examined on test cases of both theoretical and practical interests, delivering accurate and stable simulation results.

Decoupled equations for reverse time migration in tilted transversely isotropic media

KAUST Repository

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

2012-01-01

Conventional modeling and migration for tilted transversely isotropic (TTI) media may suffer from numerical instabilities and shear wave artifacts due to the coupling of the P-wave and SV-wave modes in the TTI coupled equations. Starting with the separated P- and SV-phase velocity expressions for vertical transversely isotropic (VTI) media, we extend these decoupled equations for modeling and reverse time migration (RTM) in acoustic TTI media. Compared with the TTI coupled equations published in the geophysical literature, the new TTI decoupled equations provide a more stable solution due to the complete separation of the P-wave and SV-wave modes. The pseudospectral method is the most convenient method to implement these equations due to the form of wavenumber expressions and has the added benefit of being highly accurate and thus avoiding numerical dispersion. The rapid expansion method (REM) in time is employed to produce a broad band numerically stable time evolution of the wavefields. Synthetic results validate the proposed TTI decoupled equations and show that modeling and RTM in TTI media with the decoupled equations remain numerically stable even for models with strong anisotropy and sharp contrasts. © 2012 Society of Exploration Geophysicists.

Decoupled equations for reverse time migration in tilted transversely isotropic media

KAUST Repository

Zhan, Ge

2012-03-01

Conventional modeling and migration for tilted transversely isotropic (TTI) media may suffer from numerical instabilities and shear wave artifacts due to the coupling of the P-wave and SV-wave modes in the TTI coupled equations. Starting with the separated P- and SV-phase velocity expressions for vertical transversely isotropic (VTI) media, we extend these decoupled equations for modeling and reverse time migration (RTM) in acoustic TTI media. Compared with the TTI coupled equations published in the geophysical literature, the new TTI decoupled equations provide a more stable solution due to the complete separation of the P-wave and SV-wave modes. The pseudospectral method is the most convenient method to implement these equations due to the form of wavenumber expressions and has the added benefit of being highly accurate and thus avoiding numerical dispersion. The rapid expansion method (REM) in time is employed to produce a broad band numerically stable time evolution of the wavefields. Synthetic results validate the proposed TTI decoupled equations and show that modeling and RTM in TTI media with the decoupled equations remain numerically stable even for models with strong anisotropy and sharp contrasts. © 2012 Society of Exploration Geophysicists.

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

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.

Spin-orbit couplings within the equation-of-motion coupled-cluster framework: Theory, implementation, and benchmark calculations

Energy Technology Data Exchange (ETDEWEB)

Epifanovsky, Evgeny [Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482 (United States); Department of Chemistry, University of California, Berkeley, California 94720 (United States); Q-Chem Inc., 6601 Owens Drive, Suite 105, Pleasanton, California 94588 (United States); Klein, Kerstin; Gauss, Jürgen [Institut für Physikalische Chemie, Universität Mainz, D-55099 Mainz (Germany); Stopkowicz, Stella [Department of Chemistry, Centre for Theoretical and Computational Chemistry, University of Oslo, N-0315 Oslo (Norway); Krylov, Anna I. [Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482 (United States)

2015-08-14

We present a formalism and an implementation for calculating spin-orbit couplings (SOCs) within the EOM-CCSD (equation-of-motion coupled-cluster with single and double substitutions) approach. The following variants of EOM-CCSD are considered: EOM-CCSD for excitation energies (EOM-EE-CCSD), EOM-CCSD with spin-flip (EOM-SF-CCSD), EOM-CCSD for ionization potentials (EOM-IP-CCSD) and electron attachment (EOM-EA-CCSD). We employ a perturbative approach in which the SOCs are computed as matrix elements of the respective part of the Breit-Pauli Hamiltonian using zeroth-order non-relativistic wave functions. We follow the expectation-value approach rather than the response-theory formulation for property calculations. Both the full two-electron treatment and the mean-field approximation (a partial account of the two-electron contributions) have been implemented and benchmarked using several small molecules containing elements up to the fourth row of the periodic table. The benchmark results show the excellent performance of the perturbative treatment and the mean-field approximation. When used with an appropriate basis set, the errors with respect to experiment are below 5% for the considered examples. The findings regarding basis-set requirements are in agreement with previous studies. The impact of different correlation treatment in zeroth-order wave functions is analyzed. Overall, the EOM-IP-CCSD, EOM-EA-CCSD, EOM-EE-CCSD, and EOM-SF-CCSD wave functions yield SOCs that agree well with each other (and with the experimental values when available). Using an EOM-CCSD approach that provides a more balanced description of the target states yields more accurate results.

Analytical solutions of coupled-mode equations for microring ...

Indian Academy of Sciences (India)

equivalent to waveguide and single microring coupled system. The 3 × 3 coupled system is equivalent to waveguide and double microring coupled system. In this paper, we adopt a novel approach for obtaining coupled-mode equations for linearly distributed and circularly distributed multiwaveguide systems with different ...

On the stability, the periodic solutions and the resolution of certain types of non linear equations, and of non linearly coupled systems of these equations, appearing in betatronic oscillations; Sur la stabilite, les solutions periodiques et la resolution de certaines categories d'equations et systemes d'equations differentielles couplees non lineaires apparaissant dans les oscillations betatroniques

Energy Technology Data Exchange (ETDEWEB)

Valat, J [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1960-12-15

Universal stability diagrams have been calculated and experimentally checked for Hill-Meissner type equations with square-wave coefficients. The study of these equations in the phase-plane has then made it possible to extend the periodic solution calculations to the case of non-linear differential equations with periodic square-wave coefficients. This theory has been checked experimentally. For non-linear coupled systems with constant coefficients, a search was first made for solutions giving an algebraic motion. The elliptical and Fuchs's functions solve such motions. The study of non-algebraic motions is more delicate, apart from the study of nonlinear Lissajous's motions. A functional analysis shows that it is possible however in certain cases to decouple the system and to find general solutions. For non-linear coupled systems with periodic square-wave coefficients it is then possible to calculate the conditions leading to periodic solutions, if the two non-linear associated systems with constant coefficients fall into one of the categories of the above paragraph. (author) [French] Pour les equations du genre de Hill-Meissner a coefficients creneles, on a calcule des diagrammes universels de stabilite et ceux-ci ont ete verifies experimentalement. L'etude de ces equations dans le plan de phase a permis ensuite d'etendre le calcul des solutions periodiques au cas des equations differentielles non lineaires a coefficients periodiques creneles. Cette theorie a ete verifiee experimentalement. Pour Jes systemes couples non lineaires a coefficients constants, on a d'abord cherche les solutions menant a des mouvements algebriques. Les fonctions elliptiques et fuchsiennes uniformisent de tels mouvements. L'etude de mouvements non algebriques est plus delicate, a part l'etude des mouvements de Lissajous non lineaires. Une analyse fonctionnelle montre qu'il est toutefois possible dans certains cas de decoupler le systeme et de trouver des solutions generales. Pour les

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.)

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.

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)

A Calderón multiplicative preconditioner for coupled surface-volume electric field integral equations

KAUST Repository

Bagci, Hakan

2010-08-01

A well-conditioned coupled set of surface (S) and volume (V) electric field integral equations (S-EFIE and V-EFIE) for analyzing wave interactions with densely discretized composite structures is presented. Whereas the V-EFIE operator is well-posed even when applied to densely discretized volumes, a classically formulated S-EFIE operator is ill-posed when applied to densely discretized surfaces. This renders the discretized coupled S-EFIE and V-EFIE system ill-conditioned, and its iterative solution inefficient or even impossible. The proposed scheme regularizes the coupled set of S-EFIE and V-EFIE using a Calderón multiplicative preconditioner (CMP)-based technique. The resulting scheme enables the efficient analysis of electromagnetic interactions with composite structures containing fine/subwavelength geometric features. Numerical examples demonstrate the efficiency of the proposed scheme. © 2006 IEEE.

Full thermomechanical coupling in modelling of micropolar thermoelasticity

Science.gov (United States)

Murashkin, E. V.; Radayev, Y. N.

2018-04-01

The present paper is devoted to plane harmonic waves of displacements and microrotations propagating in fully coupled thermoelastic continua. The analysis is carried out in the framework of linear conventional thermoelastic micropolar continuum model. The reduced energy balance equation and the special form of the Helmholtz free energy are discussed. The constitutive constants providing fully coupling of equations of motion and heat conduction are considered. The dispersion equation is derived and analysed in the form bi-cubic and bi-quadratic polynoms product. The equation are analyzed by the computer algebra system Mathematica. Algebraic forms expressed by complex multivalued square and cubic radicals are obtained for wavenumbers of transverse and longitudinal waves. The exact forms of wavenumbers of a plane harmonic coupled thermoelastic waves are computed.

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.

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...

Integrable parameter regimes and stationary states of nonlinearly coupled electromagnetic and ion-acoustic waves

International Nuclear Information System (INIS)

Rao, N.N.

1998-01-01

A systematic analysis of the stationary propagation of nonlinearly coupled electromagnetic and ion-acoustic waves in an unmagnetized plasma via the ponderomotive force is carried out. For small but finite amplitudes, the governing equations have a Hamiltonian structure, but with a kinetic energy term that is not positive definite. The Hamiltonian is similar to the well-known Hacute enon endash Heiles Hamiltonian of nonlinear dynamics, and is completely integrable in three regimes of the allowed parameter space. The corresponding second invariants of motion are also explicitly obtained. The integrable parameter regimes correspond to supersonic values of the Mach number, which characterizes the propagation speed of the coupled waves. On the other hand, in the sub- as well as near-sonic regimes, the coupled mode equations admit different types of exact analytical solutions, which represent nonlinear localized eigenstates of the electromagnetic field trapped in the density cavity due to the ponderomotive potential. While the density cavity has always a single-dip structure, for larger amplitudes it can support higher-order modes having a larger number of nodes in the electromagnetic field. In particular, we show the existence of a new type of localized electromagnetic wave whose field intensity has a triple-hump structure. For typical parameter values, the triple-hump solitons propagate with larger Mach numbers that are closer to the sonic limit than the single- as well as the double-hump solitons, but carry a lesser amount of the electromagnetic field energy. A comparison between the different types of solutions is carried out. The possibility of the existence of trapped electromagnetic modes having a larger number of humps is also discussed. copyright 1998 American Institute of Physics

Coupled seismic and electromagnetic wave propagation

NARCIS (Netherlands)

Schakel, M.D.

2011-01-01

Coupled seismic and electromagnetic wave propagation is studied theoretically and experimentally. This coupling arises because of the electrochemical double layer, which exists along the solid-grain/fluid-electrolyte boundaries of porous media. Within the double layer, charge is redistributed,

Acoustic wave propagation in fluids with coupled chemical reactions

International Nuclear Information System (INIS)

Margulies, T.S.; Schwarz, W.H.

1984-08-01

This investigation presents a hydroacoustic theory which accounts for sound absorption and dispersion in a multicomponent mixture of reacting fluids (assuming a set of first-order acoustic equations without diffusion) such that several coupled reactions can occur simultaneously. General results are obtained in the form of a biquadratic characteristic equation (called the Kirchhoff-Langevin equation) for the complex propagation variable chi = - (α + iω/c) in which α is the attenuation coefficient, c is the phase speed of the progressive wave and ω is the angular frequency. Computer simulations of sound absorption spectra have been made for three different chemical systems, each comprised of two-step chemical reactions using physico-chemical data available in the literature. The chemical systems studied include: (1) water-dioxane, (2) aqueous solutions of glycine and (3) cobalt polyphosphate mixtures. Explicit comparisons are made between the exact biquadratic characteristic solution and the approximate equation (sometimes referred to as a Debye equation) previously applied to interpret the experimental data for the chemical reaction contribution to the absorption versus frequency. The relative chemical reaction and classical viscothermal contributions to the sound absorption are also presented. Several discrepancies that can arise when estimating thermodynamic data (chemical reaction heats or volume changes) for multistep chemical reaction systems when making dilute solution or constant density assumptions are discussed

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.

Traveling waves in a free-electron laser with an electromagnetic wiggler

International Nuclear Information System (INIS)

Olumi, Mohsen; Maraghechi, B; Rouhani, M H

2011-01-01

The propagation of electromagnetic traveling wave in a free-electron laser (FEL) with an electromagnetic wiggler is investigated using the relativistic fluid-Maxwell formulation. By adapting the traveling-wave ansatz, three coupled, nonlinear ordinary differential equations are obtained describing the nonlinear propagation of the coupled wave. These equations may be used to study saturation in FELs. By linearizing the nonlinear equations dispersion relations for the traveling wave are obtained. Numerical solution of the small-signal traveling dispersion relation reveals the coupling of radiation to both slow and fast space-charge waves. It is shown that the traveling wave, which is not a normal mode in a laboratory frame, becomes a normal mode in terms of a transformed variable.

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

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)

Slow wave antenna coupling to ion Bernstein waves for plasma heating in ICRF

International Nuclear Information System (INIS)

Sy, W.N-C.; Amano, T.; Ando, R.; Fukuyama, A.; Watari, T.

1984-10-01

The coupling of ICRF power from a slow wave antenna to a plasma with finite temperature is examined theoretically and compared to an independent computer calculation. It is shown that such antennas can be highly efficient in trasferring most of the antenna power directly to ion Bernstein waves, with only a very small fraction going into fast waves. The potentiality of this coupling scheme for plasma heating in ICRF is briefly discussed. (author)

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...

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

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

Quantum chaos induced by nonadiabatic coupling in wave-packet dynamics

International Nuclear Information System (INIS)

Higuchi, Hisashi; Takatsuka, Kazuo

2002-01-01

The effect of nonadiabatic coupling due to breakdown of the Born-Oppenheimer approximation on chaos is investigated. A couple of measures (indicators) that detect the extent of chaos in wave-packet dynamics on coupled potential functions are devised. Using them, we show that chaos is indeed induced by a nonadiabatic coupling in individual time-dependent wave-packet dynamics. This chaos is genuinely of quantum nature, since it arises from bifurcation and merging of a wave packet at the quasicrossing region of two coupled potential functions

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.

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

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

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.

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...

Adaptive observer for the joint estimation of parameters and input for a coupled wave PDE and infinite dimensional ODE system

KAUST Repository

Belkhatir, Zehor; Mechhoud, Sarra; Laleg-Kirati, Taous-Meriem

2016-01-01

This paper deals with joint parameters and input estimation for coupled PDE-ODE system. The system consists of a damped wave equation and an infinite dimensional ODE. This model describes the spatiotemporal hemodynamic response in the brain

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)

Ponderomotive force effects on slow-wave coupling

International Nuclear Information System (INIS)

Wilson, J.R.; Wong, K.L.

1982-01-01

Localized plasma density depressions are observed to form near a multi-ring slow-wave structure when the value of the nonlinearity parameter, s = ω 2 /sub p/eVertical BarE/sub z/Vertical Bar 2 /8πω 2 nkappaT, is of order unity. Consequent changes in the wave propagation and coupling efficiency are reported. For large enough values of s, the coupling efficiency may be reduced by 50% from the linear value

Coupled-channel equations and off-shell transformations in many-body scattering

International Nuclear Information System (INIS)

Cattapan, G.; Vanzani, V.

1977-01-01

The general structure and the basic features of several many-body coupled-channel integral equations, obtained by means of the channel coupling array device, are studied in a systematic way. Particular attention is paid to the employment of symmetric transition operators. The connection between different formulations has been clarified and the role played by some off-shell transformations for many-body transition operators has been discussed. Specific choices of the coupling scheme are considered and the corresponding coupled equations are compared with similar equations previously derived. Several sets of linear relations between transition operators have also been presented and used in a three-body context to derive uncoupled integral equations with connected kernel

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...

Resonant excitation of coupled Rayleigh waves in a short and narrow fluid channel clad between two identical metal plates

Directory of Open Access Journals (Sweden)

Victor M. García-Chocano

2011-12-01

Full Text Available Transmission of ultrasonic waves through a slit between two water immersed brass plates is studied for sub-wavelength plate thicknesses and slit apertures. Extraordinary high absorption is observed at discrete frequencies corresponding to resonant excitation of Rayleigh waves on the both sides of the channel. The coupling of the Rayleigh waves occurs through the fluid and the corresponding contribution to the dispersion has been theoretically derived and also experimentally confirmed. Symmetric and anti-symmetric modes are predicted but only the symmetric mode resonances have been observed. It follows from the dispersion equation that the coupled Rayleigh waves cannot be excited in a channel with apertures less than the critical one. The calculated critical aperture is in a good agreement with the measured acoustic spectra. These findings could be applied to design a broadband absorptive metamaterial.

Vortices at the magnetic equator generated by hybrid Alfvén resonant waves

Science.gov (United States)

Hiraki, Yasutaka

2015-01-01

We performed three-dimensional magnetohydrodynamic simulations of shear Alfvén waves in a full field line system with magnetosphere-ionosphere coupling and plasma non-uniformities. Feedback instability of the Alfvén resonant modes showed various nonlinear features under the field line cavities: (i) a secondary flow shear instability occurs at the magnetic equator, (ii) trapping of the ionospheric Alfvén resonant modes facilitates deformation of field-aligned current structures, and (iii) hybrid Alfvén resonant modes grow to cause vortices and magnetic oscillations around the magnetic equator. Essential features in the initial brightening of auroral arc at substorm onsets could be explained by the dynamics of Alfvén resonant modes, which are the nature of the field line system responding to a background rapid change.

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

Linear waves and instabilities

International Nuclear Information System (INIS)

Bers, A.

1975-01-01

The electrodynamic equations for small-amplitude waves and their dispersion relation in a homogeneous plasma are outlined. For such waves, energy and momentum, and their flow and transformation, are described. Perturbation theory of waves is treated and applied to linear coupling of waves, and the resulting instabilities from such interactions between active and passive waves. Linear stability analysis in time and space is described where the time-asymptotic, time-space Green's function for an arbitrary dispersion relation is developed. The perturbation theory of waves is applied to nonlinear coupling, with particular emphasis on pump-driven interactions of waves. Details of the time--space evolution of instabilities due to coupling are given. (U.S.)

Coupling and reduction of the HAWC equations

DEFF Research Database (Denmark)

Nim, E.

2001-01-01

This report contains a description of a general method for coupling and reduction of the so-called HAWC equations, which constitute the basis equations of motion of the aeroelastic model HAWC used widely by research institutes and industrial companies formore than the ten years. The principal aim....... In addition, the method enables the reduction of the number of degrees of freedom of the structure in order to increase the calculation efficiency and improve thecondition of the system.......This report contains a description of a general method for coupling and reduction of the so-called HAWC equations, which constitute the basis equations of motion of the aeroelastic model HAWC used widely by research institutes and industrial companies formore than the ten years. The principal aim...... of the work has been to enable the modelling wind turbines with large displacements of the blades in order to predict phenomena caused by geometric non-linear effects. However, the method can also be applied tomodel the nacelle/shaft structure of a turbine more detailed than the present HAWC model...

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…

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

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.

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.

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

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.

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.

Nonlinear transient waves in coupled phase oscillators with inertia.

Science.gov (United States)

Jörg, David J

2015-05-01

Like the inertia of a physical body describes its tendency to resist changes of its state of motion, inertia of an oscillator describes its tendency to resist changes of its frequency. Here, we show that finite inertia of individual oscillators enables nonlinear phase waves in spatially extended coupled systems. Using a discrete model of coupled phase oscillators with inertia, we investigate these wave phenomena numerically, complemented by a continuum approximation that permits the analytical description of the key features of wave propagation in the long-wavelength limit. The ability to exhibit traveling waves is a generic feature of systems with finite inertia and is independent of the details of the coupling function.

Hamiltonian aspects of three-wave resonant interactions in gas dynamics

Science.gov (United States)

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

1997-06-01

Equations describing three-wave resonant interactions in adiabatic gas dynamics in one Cartesian space dimension derived by Majda and Rosales are expressed in terms of Lagrangian and Hamiltonian variational principles. The equations consist of two coupled integro-differential Burgers equations for the backward and forward sound waves that are coupled by integral terms that describe the resonant reflection of a sound wave off an entropy wave disturbance to produce a reverse sound wave. Similarity solutions and conservation laws for the equations are derived using symmetry group methods for the special case where the entropy disturbance consists of a periodic saw-tooth profile. The solutions are used to illustrate the interplay between the nonlinearity represented by the Burgers self-wave interaction terms and wave dispersion represented by the three-wave resonant interaction terms. Hamiltonian equations in Fourier (p,t) space are also obtained where p is the Fourier space variable corresponding to the fast phase variable 0305-4470/30/12/013/img6 of the waves. The latter equations are transformed to normal form in order to isolate the normal modes of the system.

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.

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.

SELF-EXCITED WAVE PROCESSES IN CHAINS OF UNIDIRECTIONALLY COUPLED IMPULSE NEURONS

Directory of Open Access Journals (Sweden)

S. D. Glyzin

2015-01-01

Full Text Available The article is devoted to the mathematical modeling of neural activity. We propose new classes of singularly perturbed differential-difference equations with delay of Volterra type. With these systems, the models as a single neuron or neural networks are described. We study attractors of ring systems of unidirectionally coupled impulse neurons in the case where the number of links in the system increases indefinitely. In order to study periodic solutions of travelling wave type of this system, some special tricks are used which reduce the existence and stability problems for cycles to the investigation of auxiliary system with impulse actions. Using this approach, we establish that the number of stable self-excited waves simultaneously existing in the chain increases unboundedly as the number of links of the chain increases, that is, the well-known buffer phenomenon occurs.

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.

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.

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.

Analytical solutions for coupling fractional partial differential equations with Dirichlet boundary conditions

Science.gov (United States)

Ding, Xiao-Li; Nieto, Juan J.

2017-11-01

In this paper, we consider the analytical solutions of coupling fractional partial differential equations (FPDEs) with Dirichlet boundary conditions on a finite domain. Firstly, the method of successive approximations is used to obtain the analytical solutions of coupling multi-term time fractional ordinary differential equations. Then, the technique of spectral representation of the fractional Laplacian operator is used to convert the coupling FPDEs to the coupling multi-term time fractional ordinary differential equations. By applying the obtained analytical solutions to the resulting multi-term time fractional ordinary differential equations, the desired analytical solutions of the coupling FPDEs are given. Our results are applied to derive the analytical solutions of some special cases to demonstrate their applicability.

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

Green function for three-wave coupling problems

International Nuclear Information System (INIS)

Molevich, N E

2001-01-01

The Green function is found for three-wave coupling problems. The function was used for analysis of parametric amplification in dissipative and active media. It is shown that the parametric increment in active media can become exponential. As an example, the nonstationary stimulated scattering of electromagnetic waves by sound and temperatures waves is considered. (nonlinear optical phenomena)

Characteristics of coupled acoustic wave propagation in metal pipe

International Nuclear Information System (INIS)

Kim, Ho Wuk; Kim, Min Soo; Lee, Sang Kwon

2008-01-01

The circular cylinder pipes are used in the many industrial areas. In this paper, the acoustic wave propagation in the pipe containing gas is researched. First of all, the theory for the coupled acoustic wave propagation in a pipe is investigated. Acoustic wave propagation in pipe can not be occurred independently between the wave of the fluid and the shell. It requires complicated analysis. However, as a special case, the coupled wave in a high density pipe containing a light density medium is corresponded closely to the uncoupled in-vacuo shell waves and to the rigid-walled duct fluid waves. The coincidence frequencies of acoustic and shell modes contribute to the predominant energy transmission. The coincidence frequency means the frequency corresponding to the coincidence of the wavenumber in both acoustic and shell. In this paper, it is assumed that the internal medium is much lighter than the pipe shell. After the uncoupled acoustic wave in the internal medium and uncoupled shell wave are considered, the coincidence frequencies are found. The analysis is successfully confirmed by the verification of the experiment using the real long steel pipe. This work verifies that the coupled wave characteristic of the shell and the fluid is occurred as predominant energy transmission at the coincidence frequencies

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

Terahertz wave generation in coupled quantum dots

International Nuclear Information System (INIS)

Ma Yu-Rong; Guo Shi-Fang; Duan Su-Qing

2012-01-01

Based on coupled quantum dots, we present an interesting optical effect in a four-level loop coupled system. Both the two upper levels and the two lower levels are designed to be almost degenerate, which induces a considerable dipole moment. The terahertz wave is obtained from the low-frequency component of the photon emission spectrum. The frequency of the terahertz wave can be controlled by tuning the energy levels via designing the nanostructure appropriately or tuning the driving laser field. A terahertz wave with adjustable frequency and considerable intensity (100 times higher than that of the Rayleigh line) can be obtained. It provides an effective scheme for a terahertz source. (condensed matter: electronic structure, electrical, magnetic, and optical properties)

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

Renormalization group equations with multiple coupling constants

International Nuclear Information System (INIS)

Ghika, G.; Visinescu, M.

1975-01-01

The main purpose of this paper is to study the renormalization group equations of a renormalizable field theory with multiple coupling constants. A method for the investigation of the asymptotic stability is presented. This method is applied to a gauge theory with Yukawa and self-quartic couplings of scalar mesons in order to find the domains of asymptotic freedom. An asymptotic expansion for the solutions which tend to the origin of the coupling constants is given

FORSIM-6, Automatic Solution of Coupled Differential Equation System

International Nuclear Information System (INIS)

Carver, M.B.; Stewart, D.G.; Blair, J.M.; Selander, W.N.

1983-01-01

1 - Description of problem or function: The FORSIM program is a versatile package which automates the solution of coupled differential equation systems. The independent variables are time, and up to three space coordinates, and the equations may be any mixture of partial and/or ordinary differential equations. The philosophy of the program is to provide a tool which will solve a system of differential equations for a user who has basic but unspecialized knowledge of numerical analysis and FORTRAN. The equations to be solved, together with the initial conditions and any special instructions, may be specified by the user in a single FORTRAN subroutine, although he may write a number of routines if this is more suitable. These are then loaded with the control routines, which perform the solution and any requested input and output. 2 - Method of solution: Partial differential equations are automatically converted into sets of coupled ordinary differential equations by variable order discretization in the spatial dimensions. These and other ordinary differential equations are integrated continuously in time using efficient variable order, variable step, error-controlled algorithms

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

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

Helicon wave coupling to a chiral-plasma column

International Nuclear Information System (INIS)

Torres-Silva, H.; Reggiani, N.; Sakanaka, P.H.

1995-01-01

Inductive helicon wave coupling to a chiro-plasma column is studied numerically. In our theoretical model, the RF current distribution of the chiro-plasma is taken into account using the constitutive relations of a chiral-plasma. Computational results based on the data of present-day helicon devices are show. In particular, we discuss the role of magnetic-field-aligned electron landau damping for the helicon wave absorption. In many a see, the numerical findings can be understood reasonably in terms of the wavenumber spectra of the helicon wave dispersion relation for slow and fast wave of a chiral-plasma. In general however, the full electromagnetic treatment is necessary in order to describe and to understand the inductive coupling in the helicon wave regime. (author). 9 refs., 1 fig

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)

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

Hydroelectromechanical modelling of a piezoelectric wave energy converter

Science.gov (United States)

Renzi, E.

2016-11-01

We investigate the hydroelectromechanical-coupled dynamics of a piezoelectric wave energy converter. The converter is made of a flexible bimorph plate, clamped at its ends and forced to motion by incident ocean surface waves. The piezoceramic layers are connected in series and transform the elastic motion of the plate into useful electricity by means of the piezoelectric effect. By using a distributed-parameter analytical approach, we couple the linear piezoelectric constitutive equations for the plate with the potential-flow equations for the surface water waves. The resulting system of governing partial differential equations yields a new hydroelectromechanical dispersion relation, whose complex roots are determined with a numerical approach. The effect of the piezoelectric coupling in the hydroelastic domain generates a system of short- and long-crested weakly damped progressive waves travelling along the plate. We show that the short-crested flexural wave component gives a dominant contribution to the generated power. We determine the hydroelectromechanical resonant periods of the device, at which the power output is significant.

High-frequency homogenization for travelling waves in periodic media.

Science.gov (United States)

Harutyunyan, Davit; Milton, Graeme W; Craster, Richard V

2016-07-01

We consider high-frequency homogenization in periodic media for travelling waves of several different equations: the wave equation for scalar-valued waves such as acoustics; the wave equation for vector-valued waves such as electromagnetism and elasticity; and a system that encompasses the Schrödinger equation. This homogenization applies when the wavelength is of the order of the size of the medium periodicity cell. The travelling wave is assumed to be the sum of two waves: a modulated Bloch carrier wave having crystal wavevector [Formula: see text] and frequency ω 1 plus a modulated Bloch carrier wave having crystal wavevector [Formula: see text] and frequency ω 2 . We derive effective equations for the modulating functions, and then prove that there is no coupling in the effective equations between the two different waves both in the scalar and the system cases. To be precise, we prove that there is no coupling unless ω 1 = ω 2 and [Formula: see text] where Λ =(λ 1 λ 2 …λ d ) is the periodicity cell of the medium and for any two vectors [Formula: see text] the product a ⊙ b is defined to be the vector ( a 1 b 1 , a 2 b 2 ,…, a d b d ). This last condition forces the carrier waves to be equivalent Bloch waves meaning that the coupling constants in the system of effective equations vanish. We use two-scale analysis and some new weak-convergence type lemmas. The analysis is not at the same level of rigour as that of Allaire and co-workers who use two-scale convergence theory to treat the problem, but has the advantage of simplicity which will allow it to be easily extended to the case where there is degeneracy of the Bloch eigenvalue.

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

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.

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.

Anomalous convection diffusion and wave coupling transport of cells on comb frame with fractional Cattaneo-Christov flux

Science.gov (United States)

Liu, Lin; Zheng, Liancun; Liu, Fawang; Zhang, Xinxin

2016-09-01

An improved Cattaneo-Christov flux model is proposed which can be used to capture the effects of the time and spatial relaxations, the time and spatial inhomogeneous diffusion and the spatial transition probability of cell transport in a highly non-homogeneous medium. Solutions are obtained by numerical discretization method where the time and spatial fractional derivative are discretized by the L1-approximation and shifted Grünwald definition, respectively. The solvability, stability and convergence of the numerical method for the special case of the Cattaneo-Christov equation are proved. Results indicate that the fractional convection diffusion-wave equation is an evolution equation which displays the coexisting characteristics of parabolicity and hyperbolicity. In other words, for α in (0, 1), the cells transport occupies the characteristics of coupling convection diffusion and wave spreading. Moreover, the effects of pertinent time parameter, time and spatial fractional derivative parameters, relaxation parameter, weight coefficient and the convection velocity on the anomalous transport of cells are shown graphically and analyzed in detail.

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

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

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

Coupled magnetoelastic waves in ferromagnetic shape-memory alloys

Science.gov (United States)

Bar'Yakhtar, V. G.; Danilevich, A. G.; L'Vov, V. A.

2011-10-01

The theory of the spectra of coupled magnetoelastic waves in ferromagnetic shape-memory alloys (FSMA) is developed. The possibility of an abnormally strong coupling of spin waves with the soft elastic mode at approaching the martensitic transformation (MT) temperature is disclosed. In particular the magnetoelastic waves in Ni-Mn-Ga single crystals are considered. A considerable (by an order of magnitude) reduction of the shear elastic modulus and an appropriate lowering of the transversal velocity of sound in the applied magnetic field are predicted. Optimum conditions for the experimental observation of the predicted effects are specified.

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.

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.

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

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

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

Three-dimensional stability of solitary kinetic Alfven waves and ion-acoustic waves

International Nuclear Information System (INIS)

Ghosh, G.; Das, K.P.

1994-01-01

Starting from a set of equations that lead to a linear dispersion relation coupling kinetic Alfven waves and ion-acoustic waves, three-dimensional KdV equations are derived for these waves. These equations are then used to investigate the three-dimensional stability of solitary kinetic Alfven waves and ion-acoustic waves by the small-k perturbation expansion method of Rowlands and Infeld. For kinetic Alfven waves it is found that there is instability if the direction of the plane-wave perturbation lies inside a cone, and the growth rate of the instability attains a maximum when the direction of the perturbation lies in the plane containing the external magnetic field and the direction of propagation of the solitary wave. For ion-acoustic waves the growth rate of instability attains a maximum when the direction of the perturbation lies in a plane perpendicular to the direction of propagation of the solitary wave. (Author)

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

Alternative integral equations and perturbation expansions for self-coupled scalar fields

International Nuclear Information System (INIS)

Ford, L.H.

1985-01-01

It is shown that the theory of a self-coupled scalar field may be expressed in terms of a class of integral equations which include the Yang-Feldman equation as a particular case. Other integral equations in this class could be used to generate alternative perturbation expansions which contain a nonanalytic dependence upon the coupling constant and are less ultraviolet divergent than the conventional perturbation expansion. (orig.)

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

The Gardner equation is a fundamental mathematical model for the description of weakly nonlinear weakly dispersive internal waves, when cubic nonlinearity cannot be neglected. Within this model coefficients of quadratic and cubic nonlinearity can both be positive as well as negative, depending on background conditions of the medium, where waves propagate (sea water density stratification, shear flow profile) [Rouvinskaya et al., 2014, Kurkina et al., 2011, 2015]. For the investigation of weakly dispersive behavior in the framework of nondimensional Gardner equation with fixed (positive) sign of quadratic nonlinearity and positive or negative cubic nonlinearity {eq1} partial η/partial t+6η( {1± η} )partial η/partial x+partial ^3η/partial x^3=0, } the series of numerical experiments of initial-value problem was carried out for evolution of a bell-shaped impulse of negative polarity (opposite to the sign of quadratic nonlinear coefficient): {eq2} η(x,t=0)=-asech2 ( {x/x0 } ), for which amplitude a and width x0 was varied. Similar initial-value problem was considered in the paper [Trillo et al., 2016] for the Korteweg - de Vries equation. For the Gardner equation with different signs of cubic nonlinearity the initial-value problem for piece-wise constant initial condition was considered in detail in [Grimshaw et al., 2002, 2010]. It is widely known, for example, [Pelinovsky et al., 2007], that the Gardner equation (1) with negative cubic nonlinearity has a family of classic solitary wave solutions with only positive polarity,and with limiting amplitude equal to 1. Therefore evolution of impulses (2) of negative polarity (whose amplitudes a were varied from 0.1 to 3, and widths at the level of a/2 were equal to triple width of solitons with the same amplitude for a 1) was going on a universal scenario with the generation of nonlinear Airy wave. For the Gardner equation (1) with the positive cubic nonlinearity coefficient there exist two one-parametric families of

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

Research of time-domain equivalent circuit method in solving dispersion of coupled-cavity traveling-wave tube

International Nuclear Information System (INIS)

Li Wenjun; China Academy of Engineering Physics, Mianyang; Xu Zhou; Li Ming; Yang Xingfan; Chen Yanan; Liu Jie; Jin Xiao; Lin Yuzheng

2008-01-01

In this paper, a time-domain equivalent circuit method is applied to solve dispersion of coupled-cavity travelling-wave tube (CCTWT). First, the time-domain circuit equations of CCTWT coupled-cavity chain are deduced from the equivalent circuit model. Then, the equations are solved numerically by fourth-order Runge-Kutta method and a program CTTDCP is developed using MATLAB. Last, a L-band CCTWT is calculated using CTTDCP and the cavity pass-band of this tube is computed to be 1.08-1.48 GHz, which is consistent with the experimental results and the simulation results of electromagnetic code and demonstrates the validity of the time-domain equivalent circuit method. In addition, a new design method which uses the equivalent circuit method and electromagnetic simulation together to optimize the cold cavity characteristics of CCTWT is proposed. (authors)

Nonlinear Waves in Complex Systems

DEFF Research Database (Denmark)

2007-01-01

The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations, it is the ......The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations...

Positive Solutions for Coupled Nonlinear Fractional Differential Equations

Directory of Open Access Journals (Sweden)

Wenning Liu

2014-01-01

Full Text Available We consider the existence of positive solutions for a coupled system of nonlinear fractional differential equations with integral boundary values. Assume the nonlinear term is superlinear in one equation and sublinear in the other equation. By constructing two cones K1, K2 and computing the fixed point index in product cone K1×K2, we obtain that the system has a pair of positive solutions. It is remarkable that it is established on the Cartesian product of two cones, in which the feature of two equations can be opposite.

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 ...

The application of He's exp-function method to a nonlinear differential-difference equation

International Nuclear Information System (INIS)

Dai Chaoqing; Cen Xu; Wu Shengsheng

2009-01-01

This paper applies He's exp-function method, which was originally proposed to find new exact travelling wave solutions of nonlinear partial differential equations (NPDEs) or coupled nonlinear partial differential equations (CNPDEs), to a nonlinear differential-difference equation, and some new travelling wave solutions are obtained.

Formation of Hydro-acoustic Waves in Dissipative Coupled Weakly Compressible Fluids

Science.gov (United States)

Abdolali, A.; Kirby, J. T., Jr.; Bellotti, G.

2014-12-01

Recent advances in deep sea measurement technology provide an increasing opportunity to detect and interpret hydro-acoustic waves as a component in improved Tsunami Early Warning Systems (TEWS). For the idealized case of a homogeneous water column above a moving but otherwise rigid bottom (in terms of assessing acoustic wave interaction), the description of the infinite family of acoustic modes is characterized by local water depth at source area; i.e. the period of the first acoustic mode is given by four times the required time for sound to travel from the seabed to the surface. Spreading off from earthquake zone, the dominant spectrum is filtered and enriched by seamounts and barriers. This study focuses on the characteristics of hydro-acoustic waves generated by sudden sea bottom motion in a weakly compressible fluid coupled with an underlying sedimentary layer, where the added complexity of the sediment layer rheology leads to both the lowering of dominant spectral peaks and wave attenuation across the full spectrum. To overcome the computational difficulties of three-dimensional models, we derive a depth integrated equation valid for varying water depth and sediment thickness. Damping behavior of the two layered system is initially taken into account by introducing the viscosity of fluid-like sedimentary layer. We show that low frequency pressure waves which are precursor components of tsunamis contain information of seafloor motion.

Calculations of non-adiabatic couplings within equation-of-motion coupled-cluster framework: Theory, implementation, and validation against multi-reference methods

Science.gov (United States)

Faraji, Shirin; Matsika, Spiridoula; Krylov, Anna I.

2018-01-01

We report an implementation of non-adiabatic coupling (NAC) forces within the equation-of-motion coupled-cluster with single and double excitations (EOM-CCSD) framework via the summed-state approach. Using illustrative examples, we compare NAC forces computed with EOM-CCSD and multi-reference (MR) wave functions (for selected cases, we also consider configuration interaction singles). In addition to the magnitude of the NAC vectors, we analyze their direction, which is important for the calculations of the rate of non-adiabatic transitions. Our benchmark set comprises three doublet radical-cations (hexatriene, cyclohexadiene, and uracil), neutral uracil, and sodium-doped ammonia clusters. When the characters of the states agree among different methods, we observe good agreement between the respective NAC vectors, both in the Franck-Condon region and away. In the cases of large discrepancies between the methods, the disagreement can be attributed to the difference in the states' character, which, in some cases, is very sensitive to electron correlation, both within single-reference and multi-reference frameworks. The numeric results confirm that the accuracy of NAC vectors depends critically on the quality of the underlying wave functions. Within their domain of applicability, EOM-CC methods provide a viable alternative to MR approaches.

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.

Shear Alfven wave excitation by direct antenna coupling and fast wave resonant mode conversion

International Nuclear Information System (INIS)

Borg, G.G.

1994-01-01

Antenna coupling to the shear Alfven wave by both direct excitation and fast wave resonant mode conversion is modelled analytically for a plasma with a one dimensional linear density gradient. We demonstrate the existence of a shear Alfven mode excited directly by the antenna. For localised antennas, this mode propagates as a guided beam along the steady magnetic field lines intersecting the antenna. Shear Alfven wave excitation by resonant mode conversion of a fast wave near the Alfven resonance layer is also demonstrated and we prove that energy is conserved in this process. We compare the efficiency of these two mechanisms of shear Alfven wave excitation and present a simple analytical formula giving the ratio of the coupled powers. Finally, we discuss the interpretation of some experimental results. 45 refs., 7 figs

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

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.

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

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.

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)

Parallel Algorithm Solves Coupled Differential Equations

Science.gov (United States)

Hayashi, A.

1987-01-01

Numerical methods adapted to concurrent processing. Algorithm solves set of coupled partial differential equations by numerical integration. Adapted to run on hypercube computer, algorithm separates problem into smaller problems solved concurrently. Increase in computing speed with concurrent processing over that achievable with conventional sequential processing appreciable, especially for large problems.

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.

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.

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.

Stability of post-fertilization traveling waves

Science.gov (United States)

Flores, Gilberto; Plaza, Ramón G.

This paper studies the stability of a family of traveling wave solutions to the system proposed by Lane et al. [D.C. Lane, J.D. Murray, V.S. Manoranjan, Analysis of wave phenomena in a morphogenetic mechanochemical model and an application to post-fertilization waves on eggs, IMA J. Math. Appl. Med. Biol. 4 (4) (1987) 309-331], to model a pair of mechanochemical phenomena known as post-fertilization waves on eggs. The waves consist of an elastic deformation pulse on the egg's surface, and a free calcium concentration front. The family is indexed by a coupling parameter measuring contraction stress effects on the calcium concentration. This work establishes the spectral, linear and nonlinear orbital stability of these post-fertilization waves for small values of the coupling parameter. The usual methods for the spectral and evolution equations cannot be applied because of the presence of mixed partial derivatives in the elastic equation. Nonetheless, exponential decay of the directly constructed semigroup on the complement of the zero eigenspace is established. We show that small perturbations of the waves yield solutions to the nonlinear equations decaying exponentially to a phase-modulated traveling wave.

Solutions of system of P1 equations without use of auxiliary differential equations coupled

International Nuclear Information System (INIS)

Martinez, Aquilino Senra; Silva, Fernando Carvalho da; Cardoso, Carlos Eduardo Santos

2000-01-01

The system of P1 equations is composed by two equations coupled itself one for the neutron flux and other for the current. Usually this system is solved by definitions of two integrals parameters, which are named slowing down densities of the flux and the current. Hence, the system P1 can be change from integral to only two differential equations. However, there are two new differentials equations that may be solved with the initial system. The present work analyzes this procedure and studies a method, which solve the P1 equations directly, without definitions of slowing down densities. (author)

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

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.

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.

Coupling atmospheric and ocean wave models for storm simulation

DEFF Research Database (Denmark)

Du, Jianting

the atmosphere must, by conservation, result in the generation of the surface waves and currents. The physics-based methods are sensitive to the choice of wind-input source function (Sin), parameterization of high-frequency wave spectra tail, and numerical cut-off frequencies. Unfortunately, literature survey......This thesis studies the wind-wave interactions through the coupling between the atmospheric model and ocean surface wave models. Special attention is put on storm simulations in the North Sea for wind energy applications in the coastal zones. The two aspects, namely storm conditions and coastal...... shows that in most wind-wave coupling systems, either the Sin in the wave model is different from the one used for the momentum flux estimation in the atmospheric model, or the methods are too sensitive to the parameterization of high-frequency spectra tail and numerical cut-off frequencies. To confront...

TRAVELING WAVE SOLUTIONS OF SOME FRACTIONAL DIFFERENTIAL EQUATIONS

Directory of Open Access Journals (Sweden)

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.

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)

The Fokker-Planck equation for coupled Brown-Néel-rotation.

Science.gov (United States)

Weizenecker, Jürgen

2018-01-22

Calculating the dynamic properties of magnetization of single-domain particles is of great importance for the tomographic imaging modality known as magnetic particle imaging (MPI). Although the assumption of instantaneous thermodynamic equilibrium (Langevin function) after application of time-dependent magnetic fields is sufficient for understanding the fundamental behavior, it is essential to consider the finite response times of magnetic particles for optimizing or analyzing various aspects, e.g. interpreting spectra, optimizing MPI sequences, developing new contrasts, and evaluating simplified models. The change in magnetization following the application of the fields is caused by two different movements: the geometric rotation of the particle and the rotation of magnetization with respect to the fixed particle axes. These individual rotations can be well described using the Langevin equations or the Fokker-Planck equation. However, because the two rotations generally exhibit interdependence, it is necessary to consider coupling between the two equations. This article shows how a coupled Fokker-Planck equation can be derived on the basis of coupled Langevin equations. Two physically equivalent Fokker-Planck equations are derived and transformed by means of an appropriate series expansion into a system of ordinary differential equations, which can be solved numerically. Finally, this system is also used to specify a system of differential equations for various limiting cases (Néel, Brown, uniaxial symmetry). Generally, the system exhibits a sparsely populated matrix and can therefore be handled well numerically.

The Fokker-Planck equation for coupled Brown-Néel-rotation

Science.gov (United States)

Weizenecker, Jürgen

2018-02-01

Calculating the dynamic properties of magnetization of single-domain particles is of great importance for the tomographic imaging modality known as magnetic particle imaging (MPI). Although the assumption of instantaneous thermodynamic equilibrium (Langevin function) after application of time-dependent magnetic fields is sufficient for understanding the fundamental behavior, it is essential to consider the finite response times of magnetic particles for optimizing or analyzing various aspects, e.g. interpreting spectra, optimizing MPI sequences, developing new contrasts, and evaluating simplified models. The change in magnetization following the application of the fields is caused by two different movements: the geometric rotation of the particle and the rotation of magnetization with respect to the fixed particle axes. These individual rotations can be well described using the Langevin equations or the Fokker-Planck equation. However, because the two rotations generally exhibit interdependence, it is necessary to consider coupling between the two equations. This article shows how a coupled Fokker-Planck equation can be derived on the basis of coupled Langevin equations. Two physically equivalent Fokker-Planck equations are derived and transformed by means of an appropriate series expansion into a system of ordinary differential equations, which can be solved numerically. Finally, this system is also used to specify a system of differential equations for various limiting cases (Néel, Brown, uniaxial symmetry). Generally, the system exhibits a sparsely populated matrix and can therefore be handled well numerically.

Integral equation for Coulomb problem

International Nuclear Information System (INIS)

Sasakawa, T.

1986-01-01

For short range potentials an inhomogeneous (homogeneous) Lippmann-Schwinger integral equation of the Fredholm type yields the wave function of scattering (bound) state. For the Coulomb potential, this statement is no more valid. It has been felt difficult to express the Coulomb wave function in a form of an integral equation with the Coulomb potential as the perturbation. In the present paper, the author shows that an inhomogeneous integral equation of a Volterra type with the Coulomb potential as the perturbation can be constructed both for the scattering and the bound states. The equation yielding the binding energy is given in an integral form. The present treatment is easily extended to the coupled Coulomb problems

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.

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.

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.

Some results on the neutron transport and the coupling of equations

International Nuclear Information System (INIS)

Bal, G.

1997-01-01

Neutron transport in nuclear reactors is well modeled by the linear Boltzmann transport equation. Its resolution is relatively easy but very expensive. To achieve whole core calculations, one has to consider simpler models, such as diffusion or homogeneous transport equations. However, the solutions may become inaccurate in particular situations (as accidents for instance). That is the reason why we wish to solve the equations on small area accurately and more coarsely on the remaining part of the core. It is than necessary to introduce some links between different discretizations or modelizations. In this note, we give some results on the coupling of different discretizations of all degrees of freedom of the integral-differential neutron transport equation (two degrees for the angular variable, on for the energy component, and two or three degrees for spatial position respectively in 2D (cylindrical symmetry) and 3D). Two chapters are devoted to the coupling of discrete ordinates methods (for angular discretization). The first one is theoretical and shows the well posing of the coupled problem, whereas the second one deals with numerical applications of practical interest (the results have been obtained from the neutron transport code developed at the R and D, which has been modified for introducing the coupling). Next, we present the nodal scheme RTN0, used for the spatial discretization. We show well posing results for the non-coupled and the coupled problems. At the end, we deal with the coupling of energy discretizations for the multigroup equations obtained by homogenization. Some theoretical results of the discretization of the velocity variable (well-posing of problems), which do not deal directly with the purposes of coupling, are presented in the annexes. (author)

Experimental measurements of Helicon wave coupling in KSTAR plasmas

Energy Technology Data Exchange (ETDEWEB)

Kim, H. J.; Wi, H. H.; Wang, S. J.; Park, S. Y.; Jeong, J. H.; Han, J. W.; Kwak, J. G.; Oh, Y. K. [National Fusion Research Institute, Daejeon (Korea, Republic of); Chun, M. H.; Yu, I. H. [Pohang Accelerator Laboratory, Pohang (Korea, Republic of)

2016-05-15

KSTAR tokamak can be a good platform to test this current drive concept because it has adequate machine parameters. Furthermore, KSTAR will have high electron beta plasmas in near future with additional ECH power. In 2015 KSTAR experiments, low-power traveling wave antenna has been designed, fabricated and installed for helicon wave coupling tests in KSTAT plasmas. In 2016 KSTAR campaign, 200 kW klystron power will be combined using three coaxial hybrid couplers and three dummy loads. High power RF will be fed into the traveling wave antenna with two coaxial feeders through two dual disk windows and 6 inch coaxial transmission line system. Current status and plan for high power helicon wave current drive system in KSTAR will be presented. Mock-up TWA antenna installed at the KSTAR reveals high couplings in both L- and H-mode plasmas. The coupling can be easily controlled by radial outer gap without degradation of plasma confinement or local gas puffing with slight decrease of plasma confinement.

Discrete coupled derivative nonlinear Schroedinger equations and their quasi-periodic solutions

International Nuclear Information System (INIS)

Geng Xianguo; Su Ting

2007-01-01

A hierarchy of nonlinear differential-difference equations associated with a discrete isospectral problem is proposed, in which a typical differential-difference equation is a discrete coupled derivative nonlinear Schroedinger equation. With the help of the nonlinearization of the Lax pairs, the hierarchy of nonlinear differential-difference equations is decomposed into a new integrable symplectic map and a class of finite-dimensional integrable Hamiltonian systems. Based on the theory of algebraic curve, the Abel-Jacobi coordinates are introduced to straighten out the corresponding flows, from which quasi-periodic solutions for these differential-difference equations are obtained resorting to the Riemann-theta functions. Moreover, a (2+1)-dimensional discrete coupled derivative nonlinear Schroedinger equation is proposed and its quasi-periodic solutions are derived

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

Nonlocal nonlinear coupling of kinetic sound waves

Directory of Open Access Journals (Sweden)

O. Lyubchyk

2014-11-01

Full Text Available We study three-wave resonant interactions among kinetic-scale oblique sound waves in the low-frequency range below the ion cyclotron frequency. The nonlinear eigenmode equation is derived in the framework of a two-fluid plasma model. Because of dispersive modifications at small wavelengths perpendicular to the background magnetic field, these waves become a decay-type mode. We found two decay channels, one into co-propagating product waves (forward decay, and another into counter-propagating product waves (reverse decay. All wavenumbers in the forward decay are similar and hence this decay is local in wavenumber space. On the contrary, the reverse decay generates waves with wavenumbers that are much larger than in the original pump waves and is therefore intrinsically nonlocal. In general, the reverse decay is significantly faster than the forward one, suggesting a nonlocal spectral transport induced by oblique sound waves. Even with low-amplitude sound waves the nonlinear interaction rate is larger than the collisionless dissipation rate. Possible applications regarding acoustic waves observed in the solar corona, solar wind, and topside ionosphere are briefly discussed.

Suppression of lower hybrid wave coupling due to the ponderomotive force

International Nuclear Information System (INIS)

Wilson, J.R.; Wong, K.L.

1980-04-01

The coupling efficiency from a slow-wave structure to lower hybrid waves is investigated experimentally. At moderate electric field strengths large edge density changes are observed. Wave trajectory modifications and departure from linear coupling are observed consistent with these changes and in good agreement with a simple nonlinear theory that includes the ponderomotive force

Rate equation analysis and non-Hermiticity in coupled semiconductor laser arrays

Science.gov (United States)

Gao, Zihe; Johnson, Matthew T.; Choquette, Kent D.

2018-05-01

Optically coupled semiconductor laser arrays are described by coupled rate equations. The coupled mode equations and carrier densities are included in the analysis, which inherently incorporate the carrier-induced nonlinearities including gain saturation and amplitude-phase coupling. We solve the steady-state coupled rate equations and consider the cavity frequency detuning and the individual laser pump rates as the experimentally controlled variables. We show that the carrier-induced nonlinearities play a critical role in the mode control, and we identify gain contrast induced by cavity frequency detuning as a unique mechanism for mode control. Photon-mediated energy transfer between cavities is also discussed. Parity-time symmetry and exceptional points in this system are studied. Unbroken parity-time symmetry can be achieved by judiciously combining cavity detuning and unequal pump rates, while broken symmetry lies on the boundary of the optical locking region. Exceptional points are identified at the intersection between broken symmetry and unbroken parity-time symmetry.

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.

Quantum adiabatic Markovian master equations

International Nuclear Information System (INIS)

Albash, Tameem; Zanardi, Paolo; Boixo, Sergio; Lidar, Daniel A

2012-01-01

We develop from first principles Markovian master equations suited for studying the time evolution of a system evolving adiabatically while coupled weakly to a thermal bath. We derive two sets of equations in the adiabatic limit, one using the rotating wave (secular) approximation that results in a master equation in Lindblad form, the other without the rotating wave approximation but not in Lindblad form. The two equations make markedly different predictions depending on whether or not the Lamb shift is included. Our analysis keeps track of the various time and energy scales associated with the various approximations we make, and thus allows for a systematic inclusion of higher order corrections, in particular beyond the adiabatic limit. We use our formalism to study the evolution of an Ising spin chain in a transverse field and coupled to a thermal bosonic bath, for which we identify four distinct evolution phases. While we do not expect this to be a generic feature, in one of these phases dissipation acts to increase the fidelity of the system state relative to the adiabatic ground state. (paper)

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.

Mediterranea Forecasting System: a focus on wave-current coupling

Science.gov (United States)

Clementi, Emanuela; Delrosso, Damiano; Pistoia, Jenny; Drudi, Massimiliano; Fratianni, Claudia; Grandi, Alessandro; Pinardi, Nadia; Oddo, Paolo; Tonani, Marina

2016-04-01

The Mediterranean Forecasting System (MFS) is a numerical ocean prediction system that produces analyses, reanalyses and short term forecasts for the entire Mediterranean Sea and its Atlantic Ocean adjacent areas. MFS became operational in the late 90's and has been developed and continuously improved in the framework of a series of EU and National funded programs and is now part of the Copernicus Marine Service. The MFS is composed by the hydrodynamic model NEMO (Nucleus for European Modelling of the Ocean) 2-way coupled with the third generation wave model WW3 (WaveWatchIII) implemented in the Mediterranean Sea with 1/16 horizontal resolution and forced by ECMWF atmospheric fields. The model solutions are corrected by the data assimilation system (3D variational scheme adapted to the oceanic assimilation problem) with a daily assimilation cycle, using a background error correlation matrix varying seasonally and in different sub-regions of the Mediterranean Sea. The focus of this work is to present the latest modelling system upgrades and the related achieved improvements. In order to evaluate the performance of the coupled system a set of experiments has been built by coupling the wave and circulation models that hourly exchange the following fields: the sea surface currents and air-sea temperature difference are transferred from NEMO model to WW3 model modifying respectively the mean momentum transfer of waves and the wind speed stability parameter; while the neutral drag coefficient computed by WW3 model is passed to NEMO that computes the turbulent component. In order to validate the modelling system, numerical results have been compared with in-situ and remote sensing data. This work suggests that a coupled model might be capable of a better description of wave-current interactions, in particular feedback from the ocean to the waves might assess an improvement on the prediction capability of wave characteristics, while suggests to proceed toward a fully

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.

Nonlinear coupled equations for electrochemical cells as developed by the general equation for nonequilibrium reversible-irreversible coupling.

Science.gov (United States)

Bedeaux, Dick; Kjelstrup, Signe; Öttinger, Hans Christian

2014-09-28

We show how the Butler-Volmer and Nernst equations, as well as Peltier effects, are contained in the general equation for nonequilibrium reversible and irreversible coupling, GENERIC, with a unique definition of the overpotential. Linear flux-force relations are used to describe the transport in the homogeneous parts of the electrochemical system. For the electrode interface, we choose nonlinear flux-force relationships. We give the general thermodynamic basis for an example cell with oxygen electrodes and electrolyte from the solid oxide fuel cell. In the example cell, there are two activated chemical steps coupled also to thermal driving forces at the surface. The equilibrium exchange current density obtains contributions from both rate-limiting steps. The measured overpotential is identified at constant temperature and stationary states, in terms of the difference in electrochemical potential of products and reactants. Away from these conditions, new terms appear. The accompanying energy flux out of the surface, as well as the heat generation at the surface are formulated, adding to the general thermodynamic basis.

Nonlinear coupled equations for electrochemical cells as developed by the general equation for nonequilibrium reversible-irreversible coupling

Science.gov (United States)

Bedeaux, Dick; Kjelstrup, Signe; Öttinger, Hans Christian

2014-09-01

We show how the Butler-Volmer and Nernst equations, as well as Peltier effects, are contained in the general equation for nonequilibrium reversible and irreversible coupling, GENERIC, with a unique definition of the overpotential. Linear flux-force relations are used to describe the transport in the homogeneous parts of the electrochemical system. For the electrode interface, we choose nonlinear flux-force relationships. We give the general thermodynamic basis for an example cell with oxygen electrodes and electrolyte from the solid oxide fuel cell. In the example cell, there are two activated chemical steps coupled also to thermal driving forces at the surface. The equilibrium exchange current density obtains contributions from both rate-limiting steps. The measured overpotential is identified at constant temperature and stationary states, in terms of the difference in electrochemical potential of products and reactants. Away from these conditions, new terms appear. The accompanying energy flux out of the surface, as well as the heat generation at the surface are formulated, adding to the general thermodynamic basis.

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

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

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.

Fully Coupled Three-Dimensional Dynamic Response of a Tension-Leg Platform Floating Wind Turbine in Waves and Wind

DEFF Research Database (Denmark)

Kumari Ramachandran, Gireesh Kumar Vasanta; Bredmose, Henrik; Sørensen, Jens Nørkær

2014-01-01

, which is a consequence of the wave-induced rotor dynamics. Loads and coupled responses are predicted for a set of load cases with different wave headings. Further, an advanced aero-elastic code, Flex5, is extended for the TLP wind turbine configuration and the response comparison with the simpler model......A dynamic model for a tension-leg platform (TLP) floating offshore wind turbine is proposed. The model includes three-dimensional wind and wave loads and the associated structural response. The total system is formulated using 17 degrees of freedom (DOF), 6 for the platform motions and 11...... for the wind turbine. Three-dimensional hydrodynamic loads have been formulated using a frequency-and direction-dependent spectrum. While wave loads are computed from the wave kinematics using Morison's equation, the aerodynamic loads are modeled by means of unsteady blade-element-momentum (BEM) theory...

Bright, dark, and mixed vector soliton solutions of the general coupled nonlinear Schrödinger equations.

Science.gov (United States)

Agalarov, Agalar; Zhulego, Vladimir; Gadzhimuradov, Telman

2015-04-01

The reduction procedure for the general coupled nonlinear Schrödinger (GCNLS) equations with four-wave mixing terms is proposed. It is shown that the GCNLS system is equivalent to the well known integrable families of the Manakov and Makhankov U(n,m)-vector models. This equivalence allows us to construct bright-bright and dark-dark solitons and a quasibreather-dark solution with unconventional dynamics: the density of the first component oscillates in space and time, whereas the density of the second component does not. The collision properties of solitons are also studied.

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

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.

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.

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

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

Exact Travelling Solutions of Discrete sine-Gordon Equation via Extended Tanh-Function Approach

International Nuclear Information System (INIS)

Dai Chaoqing; Zhang Jiefang

2006-01-01

In this paper, we generalize the extended tanh-function approach, which was used to find new exact travelling wave solutions of nonlinear partial differential equations or coupled nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, two series of exact travelling wave solutions of the discrete sine-Gordon equation are obtained by means of the extended tanh-function approach.

Stimulated Raman scattering and ion dynamics: the role of Langmuir wave non-linearities

International Nuclear Information System (INIS)

Bonnaud, G.; Pesme, D.

1988-02-01

The non-linear evolution of stimulated Raman scattering by coupling of the SRS-driven Langmuir waves to ion acoustic waves is studied numerically, in a homogeneous density laser-irradiated plasma. The coupled wave amplitude behaviour is represented either by envelope equations or by complete wave-like equations. The various physical phenomena which are involved are described. This preliminary work has been presented at the 17th Anomalous Absorption Conference, held in last May, in Lake Tahoe City (USA) [fr

New analytic solutions of stochastic coupled KdV equations

International Nuclear Information System (INIS)

Dai Chaoqing; Chen Junlang

2009-01-01

In this paper, firstly, we use the exp-function method to seek new exact solutions of the Riccati equation. Then, with the help of Hermit transformation, we employ the Riccati equation and its new exact solutions to find new analytic solutions of the stochastic coupled KdV equation in the white noise environment. As some special examples, some analytic solutions can degenerate into these solutions reported in open literatures.

Coupling of WRF meteorological model to WAM spectral wave model through sea surface roughness at the Balearic Sea: impact on wind and wave forecasts

Science.gov (United States)

Tolosana-Delgado, R.; Soret, A.; Jorba, O.; Baldasano, J. M.; Sánchez-Arcilla, A.

2012-04-01

Meteorological models, like WRF, usually describe the earth surface characteristics by tables that are function of land-use. The roughness length (z0) is an example of such approach. However, over sea z0 is modeled by the Charnock (1955) relation, linking the surface friction velocity u*2 with the roughness length z0 of turbulent air flow, z0 = α-u2* g The Charnock coefficient α may be considered a measure of roughness. For the sea surface, WRF considers a constant roughness α = 0.0185. However, there is evidence that sea surface roughness should depend on wave energy (Donelan, 1982). Spectral wave models like WAM, model the evolution and propagation of wave energy as a function of wind, and include a richer sea surface roughness description. Coupling WRF and WAM is thus a common way to improve the sea surface roughness description of WRF. WAM is a third generation wave model, solving the equation of advection of wave energy subject to input/output terms of: wind growth, energy dissipation and resonant non-linear wave-wave interactions. Third generation models work on the spectral domain. WAM considers the Charnock coefficient α a complex yet known function of the total wind input term, which depends on the wind velocity and on the Charnock coefficient again. This is solved iteratively (Janssen et al., 1990). Coupling of meteorological and wave models through a common Charnock coefficient is operationally done in medium-range met forecasting systems (e.g., at ECMWF) though the impact of coupling for smaller domains is not yet clearly assessed (Warner et al, 2010). It is unclear to which extent the additional effort of coupling improves the local wind and wave fields, in comparison to the effects of other factors, like e.g. a better bathymetry and relief resolution, or a better circulation information which might have its influence on local-scale meteorological processes (local wind jets, local convection, daily marine wind regimes, etc.). This work, within the

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.

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.

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.

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.

''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

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

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

Effective equations for matter-wave gap solitons in higher-order transversal states.

Science.gov (United States)

Mateo, A Muñoz; Delgado, V

2013-10-01

We demonstrate that an important class of nonlinear stationary solutions of the three-dimensional (3D) Gross-Pitaevskii equation (GPE) exhibiting nontrivial transversal configurations can be found and characterized in terms of an effective one-dimensional (1D) model. Using a variational approach we derive effective equations of lower dimensionality for BECs in (m,n(r)) transversal states (states featuring a central vortex of charge m as well as n(r) concentric zero-density rings at every z plane) which provides us with a good approximate solution of the original 3D problem. Since the specifics of the transversal dynamics can be absorbed in the renormalization of a couple of parameters, the functional form of the equations obtained is universal. The model proposed finds its principal application in the study of the existence and classification of 3D gap solitons supported by 1D optical lattices, where in addition to providing a good estimate for the 3D wave functions it is able to make very good predictions for the μ(N) curves characterizing the different fundamental families. We have corroborated the validity of our model by comparing its predictions with those from the exact numerical solution of the full 3D GPE.

Shear Wave Generation by Decoupled and Partially Coupled Explosions

National Research Council Canada - National Science Library

Stevens, Jeffry L; Xu, Heming; Baker, G. E

2008-01-01

The objective of this project is to investigate the sources of shear wave generation by decoupled and partially coupled explosions, and the differences in shear wave generation between tamped and decoupled explosions...

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)

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.

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.

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

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

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.

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

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.

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.

Transition behaviours in two coupled Josephson junction equations

International Nuclear Information System (INIS)

Wang Jiazeng; Zhang Xuejuan; You Gongqiang; Zhou Fengyan

2007-01-01

The dynamics of two coupled Josephson junction equations are investigated via mathematical reasoning and numerical simulations. We show that for a fixed coupling K, the whole parameter space can be comparted into three regions: a quenching region, a synchronized running periodic region and a region where these two states coexist. It is further shown that with the increase of the coupling K, the system may transit from a synchronizing state to a quenching state. The characteristic of the critical line K*(b) which separates these two states is mathematically analysed

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

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.

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.

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

Stimulated scattering of electromagnetic waves carrying orbital angular momentum in quantum plasmas.

Science.gov (United States)

Shukla, P K; Eliasson, B; Stenflo, L

2012-07-01

We investigate stimulated scattering instabilities of coherent circularly polarized electromagnetic (CPEM) waves carrying orbital angular momentum (OAM) in dense quantum plasmas with degenerate electrons and nondegenerate ions. For this purpose, we employ the coupled equations for the CPEM wave vector potential and the driven (by the ponderomotive force of the CPEM waves) equations for the electron and ion plasma oscillations. The electrons are significantly affected by the quantum forces (viz., the quantum statistical pressure, the quantum Bohm potential, as well as the electron exchange and electron correlations due to electron spin), which are included in the framework of the quantum hydrodynamical description of the electrons. Furthermore, our investigation of the stimulated Brillouin instability of coherent CPEM waves uses the generalized ion momentum equation that includes strong ion coupling effects. The nonlinear equations for the coupled CPEM and quantum plasma waves are then analyzed to obtain nonlinear dispersion relations which exhibit stimulated Raman, stimulated Brillouin, and modulational instabilities of CPEM waves carrying OAM. The present results are useful for understanding the origin of scattered light off low-frequency density fluctuations in high-energy density plasmas where quantum effects are eminent.

Nonlinear dynamics of resistive electrostatic drift waves

DEFF Research Database (Denmark)

Korsholm, Søren Bang; Michelsen, Poul; Pécseli, H.L.

1999-01-01

The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which is pertur......The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which...... polarity, i.e. a pair of electrostatic convective cells....

Global analysis of ICRF wave coupling on Tore Supra

International Nuclear Information System (INIS)

Goniche, M.; Bremond, S.; Colas, L.

2003-01-01

The Tore Supra tokamak is equipped with a multi-megawatt ion cyclotron range of frequency (ICRF) system for heating and current drive. The coupling of the fast wave to the plasma, characterized by the distributed coupling resistance along the radiating straps, is a crucial issue in order to launch large RF powers. Many factors can have an effect on ICRF wave coupling. Quantitative prediction from theoretical modelling requires the knowledge of the local inhomogeneous plasma density profile in front of the antenna for running sophisticated antenna codes. In this work, we have rather followed a 'global' approach, based on Tore Supra experimental results, for the parametric study of the coupling resistance. From a large data base covering seven experimental campaigns (∼2250 shots), a scaling law of the coupling resistance including the main parameters of the plasma and of the antenna configuration is established. This approach is found to be reliable for the analysis of coupling in the different scenarios: He/D 2 gas filling, gas/pellets for plasma fuelling, plasma leaning on inner wall/low field side limiter, limiter/ergodic divertor configuration, minority heating/direct electron heating. From one scenario to another, a significant variation of the coefficients of the scaling law is found. The study of these variations allows to get some insight on the main physical mechanisms which influence the ICRF wave coupling in a tokamak operation, such as the wall conditioning and recycling conditions, RF sheaths or frequency. (author)

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.

Parasitic excitation of ion Bernstein waves from a Faraday shielded fast wave loop antenna

International Nuclear Information System (INIS)

Skiff, F.; Ono, M.; Colestock, P.; Wong, K.L.

1984-12-01

Parasitic excitation of ion Bernstein waves is observed from a Faraday shielded fast wave loop antenna in the ion cyclotron frequency range. Local analysis of the Vlasov-Maxwell equations demonstrates the role of plasma density gradient in the coupling process. The effects of plasma density and of parallel wave number on the excitation process are investigated

Soliton Compton Mass from Auto-Parametric Wave-Soliton Coupling

CERN Document Server

Binder, B

2002-01-01

In this paper a self-excited Rayleigh-type system models the auto-parametric wave-soliton coupling via phase fluctuations. The parameter of dissipative terms determine not only the most likely quantum coupling between solitons and linear waves but also the most likely mass of the solitons. Phase fluctuations are mediated by virtual photons coupling at light-velocity in a permanent Compton scattering process. With a reference to the SI-units and proper scaling relations in length and velocity, the final result shows a highly interesting sequence: the likely soliton Compton mass is about 1.00138 times the neutron and 1.00276 times the proton mass.

CPDS3, Coupled 3-D Partial Differential Equation Solution

International Nuclear Information System (INIS)

Anderson, D.V.; Koniges, A.E.; Shumaker, D.E.

1992-01-01

1 - Description of program or function: CPDES3 solves the linear asymmetric matrix equations arising from coupled partial differential equations in three dimensions. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximation employed. CPDES3 allows each spatial operator to have 7, 15, 19, or 27 point stencils, permits general couplings between all of the component PDE's, and automatically generates the matrix structures needed to perform the algorithm. 2 - Method of solution: The resulting sparse matrix equation with a complicated sub-band structure and generally asymmetric is solved by either the preconditioned conjugate gradient (CG) method or the preconditioned bi-conjugate gradient (BCG) algorithm. BCG enjoys faster convergence in most cases but in rare instances diverges. Then, CG iterations must be used. 3 - Restrictions on the complexity of the problem: The discretization of the coupled three-dimensional PDE's and their boundary conditions must result in an operator stencil which fits in the Cray2 memory. In addition, the matrix must possess a reasonable amount of diagonal dominance for the preconditioning technique to be effective

CPDES2, Coupled 2-D Partial Differential Equation Solution

International Nuclear Information System (INIS)

Anderson, D.V.; Koniges, A.E.; Shumaker, D.E.

1992-01-01

1 - Description of program or function: CPDES2 solves the linear asymmetric equations arising from coupled partial differential equations in two dimensions. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximation employed. CPDES2 allows each spatial operator to have 5 or 9 point stencils, permits general coupling between all of the component PDE's, and automatically generates the matrix structures needed to perform the algorithm. 2 - Method of solution: The resulting sparse matrix equation with a complicated sub-band structure and generally asymmetric is solved by either the preconditioned conjugate gradient (CG) method or the preconditioned bi-conjugate gradient (BCG) algorithm. BCG enjoys faster convergence in most cases but in rare instances diverges. Then, CG iterations must be used. 3 - Restrictions on the complexity of the problem: The discretization of the coupled two-dimensional PDE's and their boundary conditions must result in an operator stencil which fits in the Cray2 memory. In addition, the matrix must possess a reasonable amount of diagonal dominance for the preconditioning technique to be effective

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.

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.

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→∞

Constructing New Discrete Integrable Coupling System for Soliton Equation by Kronecker Product

International Nuclear Information System (INIS)

Yu Fajun; Zhang Hongqing

2008-01-01

It is shown that the Kronecker product can be applied to constructing new discrete integrable coupling system of soliton equation hierarchy in this paper. A direct application to the fractional cubic Volterra lattice spectral problem leads to a novel integrable coupling system of soliton equation hierarchy. It is also indicated that the study of discrete integrable couplings by using the Kronecker product is an efficient and straightforward method. This method can be used generally

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.

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.

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...

''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

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

Solving the Coupled System Improves Computational Efficiency of the Bidomain Equations

KAUST Repository

Southern, J.A.

2009-10-01

The bidomain equations are frequently used to model the propagation of cardiac action potentials across cardiac tissue. At the whole organ level, the size of the computational mesh required makes their solution a significant computational challenge. As the accuracy of the numerical solution cannot be compromised, efficiency of the solution technique is important to ensure that the results of the simulation can be obtained in a reasonable time while still encapsulating the complexities of the system. In an attempt to increase efficiency of the solver, the bidomain equations are often decoupled into one parabolic equation that is computationally very cheap to solve and an elliptic equation that is much more expensive to solve. In this study, the performance of this uncoupled solution method is compared with an alternative strategy in which the bidomain equations are solved as a coupled system. This seems counterintuitive as the alternative method requires the solution of a much larger linear system at each time step. However, in tests on two 3-D rabbit ventricle benchmarks, it is shown that the coupled method is up to 80% faster than the conventional uncoupled method-and that parallel performance is better for the larger coupled problem.

Solving the Coupled System Improves Computational Efficiency of the Bidomain Equations

KAUST Repository

Southern, J.A.; Plank, G.; Vigmond, E.J.; Whiteley, J.P.

2009-01-01

The bidomain equations are frequently used to model the propagation of cardiac action potentials across cardiac tissue. At the whole organ level, the size of the computational mesh required makes their solution a significant computational challenge. As the accuracy of the numerical solution cannot be compromised, efficiency of the solution technique is important to ensure that the results of the simulation can be obtained in a reasonable time while still encapsulating the complexities of the system. In an attempt to increase efficiency of the solver, the bidomain equations are often decoupled into one parabolic equation that is computationally very cheap to solve and an elliptic equation that is much more expensive to solve. In this study, the performance of this uncoupled solution method is compared with an alternative strategy in which the bidomain equations are solved as a coupled system. This seems counterintuitive as the alternative method requires the solution of a much larger linear system at each time step. However, in tests on two 3-D rabbit ventricle benchmarks, it is shown that the coupled method is up to 80% faster than the conventional uncoupled method-and that parallel performance is better for the larger coupled problem.

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.

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

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.

Coupling of neutron transport equations. First results; Couplage d`equations en transport neutronique. premiere approche 1D monocinetique

Energy Technology Data Exchange (ETDEWEB)

Bal, G.

1995-07-01

To achieve whole core calculations of the neutron transport equation, we have to follow this 2 step method: space and energy homogenization of the assemblies; resolution of the homogenized equation on the whole core. However, this is no more valid when accidents occur (for instance depressurization causing locally strong heterogeneous media). One solution consists then in coupling two kinds of resolutions: a fine computation on the damaged cell (fine mesh, high number of energy groups) coupled with a coarse one everywhere else. We only deal here with steady state solutions (which already live in 6D spaces). We present here two such methods: The coupling by transmission of homogenized sections and the coupling by transmission of boundary conditions. To understand what this coupling is, we first restrict ourselves to 1D with respect to space in one energy group. The first two chapters deal with a recall of basic properties of the neutron transport equation. We give at chapter 3 some indications of the behaviour of the flux with respect to the cross sections. We present at chapter 4 some couplings and give some properties. Chapter 5 is devoted to a presentation of some numerical applications. (author). 9 refs., 7 figs.