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.

A perturbative solution for gravitational waves in quadratic gravity

International Nuclear Information System (INIS)

Neto, Edgard C de Rey; Aguiar, Odylio D; Araujo, Jose C N de

2003-01-01

We find a gravitational wave solution to the linearized version of quadratic gravity by adding successive perturbations to Einstein's linearized field equations. We show that only the Ricci-squared quadratic invariant contributes to give a different solution to those found in Einstein's general relativity. The perturbative solution is written as a power series in the β parameter, the coefficient of the Ricci-squared term in the quadratic gravitational action. We also show that, for monochromatic waves of a given angular frequency ω, the perturbative solution can be summed out to give an exact solution to the linearized version of quadratic gravity, for 0 1/2 . This result may lead to implications for the predictions for gravitational wave backgrounds of cosmological origin

Perturbed soliton excitations of Rao-dust Alfvén waves in magnetized dusty plasmas

Energy Technology Data Exchange (ETDEWEB)

Kavitha, L., E-mail: louiskavitha@yahoo.co.in [Department of Physics, School of Basic and Applied Sciences, Central University of Tamil Nadu, Thiruvarur 610 101 (India); The Abdus Salam International Centre for Theoretical Physics, Trieste (Italy); Lavanya, C.; Senthil Kumar, V. [Department of Physics, Periyar University, Salem, Tamil Nadu 636 011 (India); Gopi, D. [Department of Chemistry, Periyar University, Salem 636 011 (India); Center for Nanoscience and Nanotechnology, Periyar University, Salem, Tamil Nadu 636 011 (India); Pasqua, A. [Department of Physics, University of Trieste, Trieste (Italy)

2016-04-15

We investigate the propagation dynamics of the perturbed soliton excitations in a three component fully ionized dusty magnetoplasma consisting of electrons, ions, and heavy charged dust particulates. We derive the governing equation of motion for the two dimensional Rao-dust magnetohydrodynamic (R-D-MHD) wave by employing the inertialess electron equation of motion, inertial ion equation of motion, the continuity equations in a plasma with immobile charged dust grains, together with the Maxwell's equations, by assuming quasi neutrality and neglecting the displacement current in Ampere's law. Furthermore, we assume the massive dust particles are practically immobile since we are interested in timescales much shorter than the dusty plasma period, thereby neglecting any damping of the modes due to the grain charge fluctuations. We invoke the reductive perturbation method to represent the governing dynamics by a perturbed cubic nonlinear Schrödinger (pCNLS) equation. We solve the pCNLS, along the lines of Kodama-Ablowitz multiple scale nonlinear perturbation technique and explored the R-D-MHD waves as solitary wave excitations in a magnetized dusty plasma. Since Alfvén waves play an important role in energy transport in driving field-aligned currents, particle acceleration and heating, solar flares, and the solar wind, this representation of R-D-MHD waves as soliton excitations may have extensive applications to study the lower part of the earth's ionosphere.

Travelling wave solutions for a singularly perturbed Burgers–KdV ...

Indian Academy of Sciences (India)

This paper concerns with the existence problem of travelling wave solutions to a singularly perturbed Burgers–KdV equation. For this, we use the dynamical systems approach, specifically, the geometric singular perturbation theory and centre manifold theory. We also numerically show approximations, in particular, for ...

expansion method and travelling wave solutions for the perturbed ...

Indian Academy of Sciences (India)

Abstract. In this paper, we construct the travelling wave solutions to the perturbed nonlinear. Schrödinger's equation (NLSE) with Kerr law non-linearity by the extended (G /G)-expansion method. Based on this method, we obtain abundant exact travelling wave solutions of NLSE with. Kerr law nonlinearity with arbitrary ...

A perturbative analysis of modulated amplitude waves in Bose-Einstein condensates

International Nuclear Information System (INIS)

Porter, Mason A.; Cvitanovic, Predrag

2004-01-01

We apply Lindstedt's method and multiple scale perturbation theory to analyze spatio-temporal structures in nonlinear Schroedinger equations and thereby study the dynamics of quasi-one-dimensional Bose-Einstein condensates with mean-field interactions. We determine the dependence of the amplitude of modulated amplitude waves on their wave number. We also explore the band structure of Bose-Einstein condensates in detail using Hamiltonian perturbation theory and supporting numerical simulations

Generalized wave operators, weighted Killing fields, and perturbations of higher dimensional spacetimes

Science.gov (United States)

Araneda, Bernardo

2018-04-01

We present weighted covariant derivatives and wave operators for perturbations of certain algebraically special Einstein spacetimes in arbitrary dimensions, under which the Teukolsky and related equations become weighted wave equations. We show that the higher dimensional generalization of the principal null directions are weighted conformal Killing vectors with respect to the modified covariant derivative. We also introduce a modified Laplace–de Rham-like operator acting on tensor-valued differential forms, and show that the wave-like equations are, at the linear level, appropriate projections off shell of this operator acting on the curvature tensor; the projection tensors being made out of weighted conformal Killing–Yano tensors. We give off shell operator identities that map the Einstein and Maxwell equations into weighted scalar equations, and using adjoint operators we construct solutions of the original field equations in a compact form from solutions of the wave-like equations. We study the extreme and zero boost weight cases; extreme boost corresponding to perturbations of Kundt spacetimes (which includes near horizon geometries of extreme black holes), and zero boost to static black holes in arbitrary dimensions. In 4D our results apply to Einstein spacetimes of Petrov type D and make use of weighted Killing spinors.

Analytic perturbation theory for screened Coulomb potential: full continuum wave function

International Nuclear Information System (INIS)

Bechler, A.; Ennan, Mc J.; Pratt, R.H.

1979-01-01

An analytic perturbation theory developed previously is used to find a continuum screened-Coulomb wave function characterized by definite asymptotic momentum. This wave function satisfies an inhomogeneous partial differential equation which is solved in parabolic coordinates; the solution depends on both parabolic variables. We calculate partial wave projections of this solution and show that we can choose to add a solution of the homogeneous equation such that the partial wave projections become equal to the normalized continuum radial function found previously. However, finding the unique solution with given asymptotic linear momentum will require either using boundary conditions to determine the unique needed solution of the homogeneous equation or equivalently specifying the screened-Coulomb phase-shifts. (author)

DENSITY PERTURBATION BY ALFVÉN WAVES IN MAGNETO-PLASMA

Energy Technology Data Exchange (ETDEWEB)

Kumar, S.; Moon, Y.-J. [School of Space Research, Kyung Hee University, Yongin, Gyeonggi-Do, 446-701 (Korea, Republic of); Sharma, R. P. [Centre for Energy Studies, Indian Institute of Technology (IIT) Delhi, Hauz Khas, New Delhi, 110016 (India)

2016-12-20

In this article, we attempt to investigate the density perturbations along magnetic field by ponderomotive effects due to inertial Alfvén waves (AWs) in auroral ionosphere. For this study, we take high-frequency inertial AWs (pump) and their nonlinear interactions with low-frequency slow modes of AWs in that region. The dynamical equations representing these wave modes are known as the Zakharov like equation, and are solved numerically. From the results presented here, we notice the density perturbations in the direction of background magnetic fields. We also find that the deepest density cavity is associated with the strongest magnetic fields. The main reason for these nonlinear structures could be the ponderomotive effects due to the pump waves. The amplitude of these density structures varies with time until the modulation instability saturates. From our results, we estimate the amplitude of most intense cavity as ∼15% of the unperturbed plasma number density n {sub 0}, which is consistent with the observations. These density structures could be the locations for particle energizations in this region.

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.

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.

Quasi-Maxwellian gravitation equations: aplication to the perturbations of the Friedmann cosmological models

International Nuclear Information System (INIS)

Salim, J.M.

1982-01-01

The perturbation theory of cosmological models, in particular Friedmann models, following the quasi-Maxwellian equations are systematically developed. Perturbations to imperfect sources are directly generalized. It is shown that Friedmann models are unstable by fluid vorticity perturbations. It is also shown that the study of gravitational waves can not be done independently of the coupling with the matter. Lifshitz results concerning matter density perturbation are found again and it is shown that some soluctions, considered in literature as physically acceptable, are naive coordinate transformations. (L.C.) [pt

On a Shallow Water Equation Perturbed in Schwartz Class

International Nuclear Information System (INIS)

Zhu Xiang’ou

2012-01-01

We discuss the Camassa-Holm equation perturbed in Schwartz class around a suitable constant. This paper is concerned with the wave breaking mechanism for periodic case where two special classes of initial data were involved. The asymptotic behavior of solutions is also analyzed in the following sense: the corresponding solution to initial data with algebraic decay at infinity will retain this property at infinity in its lifespan.

Solving the Helmholtz equation in conformal mapped ARROWstructures using homotopy perturbation method

DEFF Research Database (Denmark)

Reck, Kasper; Thomsen, Erik Vilain; Hansen, Ole

2011-01-01

. The solution of the mapped Helmholtz equation is found by solving an infinite series of Poisson equations using two dimensional Fourier series. The solution is entirely based on analytical expressions and is not mesh dependent. The analytical results are compared to a numerical (finite element method) solution......The scalar wave equation, or Helmholtz equation, describes within a certain approximation the electromagnetic field distribution in a given system. In this paper we show how to solve the Helmholtz equation in complex geometries using conformal mapping and the homotopy perturbation method...

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→∞

Singularly perturbed volterra integro-differential equations | Bijura ...

African Journals Online (AJOL)

Several investigations have been made on singularly perturbed integral equations. This paper aims at presenting an algorithm for the construction of asymptotic solutions and then provide a proof asymptotic correctness to singularly perturbed systems of Volterra integro-differential equations. Mathematics Subject

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.

Perturbed Coulomb Potentials in the Klein-Gordon Equation: Quasi-Exact Solution

Science.gov (United States)

Baradaran, M.; Panahi, H.

2018-05-01

Using the Lie algebraic approach, we present the quasi-exact solutions of the relativistic Klein-Gordon equation for perturbed Coulomb potentials namely the Cornell potential, the Kratzer potential and the Killingbeck potential. We calculate the general exact expressions for the energies, corresponding wave functions and the allowed values of the parameters of the potential within the representation space of sl(2) Lie algebra. In addition, we show that the considered equations can be transformed into the Heun's differential equations and then we reproduce the results using the associated special functions. Also, we study the special case of the Coulomb potential and show that in the non-relativistic limit, the solution of the Klein-Gordon equation converges to that of Schrödinger equation.

Application of perturbation theory to a P-wave eikonal equation in orthorhombic media

KAUST Repository

Stovas, Alexey; Masmoudi, Nabil; Alkhalifah, Tariq Ali

2016-01-01

The P-wave eikonal equation for orthorhombic (ORT) anisotropic media is a highly nonlinear partial differential equation requiring the solution of a sixth-order polynomial to obtain traveltimes, resulting in complex and time-consuming numerical

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

International Nuclear Information System (INIS)

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

1980-01-01

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

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

On the singular perturbations for fractional differential equation.

Science.gov (United States)

Atangana, Abdon

2014-01-01

The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

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

On the Singular Perturbations for Fractional Differential Equation

Directory of Open Access Journals (Sweden)

Abdon Atangana

2014-01-01

Full Text Available The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

Painleve analysis, conservation laws, and symmetry of perturbed nonlinear equations

International Nuclear Information System (INIS)

Basak, S.; Chowdhury, A.R.

1987-01-01

The authors consider the Lie-Backlund symmetries and conservation laws of a perturbed KdV equation and NLS equation. The arbitrary coefficients of the perturbing terms can be related to the condition of existence of nontrivial LB symmetry generators. When the perturbed KdV equation is subjected to Painleve analysis a la Weiss, it is found that the resonance position changes compared to the unperturbed one. They prove the compatibility of the overdetermined set of equations obtained at the different stages of recursion relations, at least for one branch. All other branches are also indicated and difficulties associated them are discussed considering the perturbation parameter epsilon to be small. They determine the Lax pair for the aforesaid branch through the use of Schwarzian derivative. For the perturbed NLS equation they determine the conservation laws following the approach of Chen and Liu. From the recurrence of these conservation laws a Lax pair is constructed. But the Painleve analysis does not produce a positive answer for the perturbed NLS equation. So here they have two contrasting examples of perturbed nonlinear equations: one passes the Painleve test and its Lax pair can be found from the analysis itself, but the other equation does not meet the criterion of the Painleve test, though its Lax pair is found in another way

Electromagnetic interactions in relativistic infinite component wave equations

International Nuclear Information System (INIS)

Gerry, C.C.

1979-01-01

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

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

Soliton solutions and chaotic motions of the Zakharov equations for the Langmuir wave in the plasma

Energy Technology Data Exchange (ETDEWEB)

Zhen, Hui-Ling; Tian, Bo, E-mail: tian-bupt@163.com; Wang, Yu-Feng; Liu, De-Yin [State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876 (China)

2015-03-15

For the interaction between the high-frequency Langmuir waves and low-frequency ion-acoustic waves in the plasma, the Zakharov equations are studied in this paper. Via the Hirota method, we obtain the soliton solutions, based on which the soliton propagation is presented. It is found that with λ increasing, the amplitude of u decreases, whereas that of v remains unchanged, where λ is the ion-acoustic speed, u is the slowly-varying envelope of the Langmuir wave, and v is the fluctuation of the equilibrium ion density. Both the head-on and bound-state interactions between the two solitons are displayed. We observe that with λ decreasing, the interaction period of u decreases, while that of v keeps unchanged. It is found that the Zakharov equations cannot admit any chaotic motions. With the external perturbations taken into consideration, the perturbed Zakharov equations are studied for us to see the associated chaotic motions. Both the weak and developed chaotic motions are investigated, and the difference between them roots in the relative magnitude of the nonlinearities and perturbations. The chaotic motions are weakened with λ increasing, or else, strengthened. Periodic motion appears when the nonlinear terms and external perturbations are balanced. With such a balance kept, one period increases with λ increasing.

Exact soliton-like solutions of perturbed phi4-equation

International Nuclear Information System (INIS)

Gonzalez, J.A.

1986-05-01

Exact soliton-like solutions of damped, driven phi 4 -equation are found. The exact expressions for the velocities of solitons are given. It is non-perturbatively proved that the perturbed phi 4 -equation has stable kink-like solutions of a new type. (author)

Two-scale approach to oscillatory singularly perturbed transport equations

CERN Document Server

Frénod, Emmanuel

2017-01-01

This book presents the classical results of the two-scale convergence theory and explains – using several figures – why it works. It then shows how to use this theory to homogenize ordinary differential equations with oscillating coefficients as well as oscillatory singularly perturbed ordinary differential equations. In addition, it explores the homogenization of hyperbolic partial differential equations with oscillating coefficients and linear oscillatory singularly perturbed hyperbolic partial differential equations. Further, it introduces readers to the two-scale numerical methods that can be built from the previous approaches to solve oscillatory singularly perturbed transport equations (ODE and hyperbolic PDE) and demonstrates how they can be used efficiently. This book appeals to master’s and PhD students interested in homogenization and numerics, as well as to the Iter community.

Non-perturbational surface-wave inversion: A Dix-type relation for surface waves

Science.gov (United States)

Haney, Matt; Tsai, Victor C.

2015-01-01

We extend the approach underlying the well-known Dix equation in reflection seismology to surface waves. Within the context of surface wave inversion, the Dix-type relation we derive for surface waves allows accurate depth profiles of shear-wave velocity to be constructed directly from phase velocity data, in contrast to perturbational methods. The depth profiles can subsequently be used as an initial model for nonlinear inversion. We provide examples of the Dix-type relation for under-parameterized and over-parameterized cases. In the under-parameterized case, we use the theory to estimate crustal thickness, crustal shear-wave velocity, and mantle shear-wave velocity across the Western U.S. from phase velocity maps measured at 8-, 20-, and 40-s periods. By adopting a thin-layer formalism and an over-parameterized model, we show how a regularized inversion based on the Dix-type relation yields smooth depth profiles of shear-wave velocity. In the process, we quantitatively demonstrate the depth sensitivity of surface-wave phase velocity as a function of frequency and the accuracy of the Dix-type relation. We apply the over-parameterized approach to a near-surface data set within the frequency band from 5 to 40 Hz and find overall agreement between the inverted model and the result of full nonlinear inversion.

Acoustic anisotropic wavefields through perturbation theory

KAUST Repository

Alkhalifah, Tariq Ali

2013-09-01

Solving the anisotropic acoustic wave equation numerically using finite-difference methods introduces many problems and media restriction requirements, and it rarely contributes to the ability to resolve the anisotropy parameters. Among these restrictions are the inability to handle media with η<0 and the presence of shear-wave artifacts in the solution. Both limitations do not exist in the solution of the elliptical anisotropic acoustic wave equation. Using perturbation theory in developing the solution of the anisotropic acoustic wave equation allows direct access to the desired limitation-free solutions, that is, solutions perturbed from the elliptical anisotropic background medium. It also provides a platform for parameter estimation because of the ability to isolate the wavefield dependency on the perturbed anisotropy parameters. As a result, I derive partial differential equations that relate changes in the wavefield to perturbations in the anisotropy parameters. The solutions of the perturbation equations represented the coefficients of a Taylor-series-type expansion of the wavefield as a function of the perturbed parameter, which is in this case η or the tilt of the symmetry axis. The expansion with respect to the symmetry axis allows use of an acoustic transversely isotropic media with a vertical symmetry axis (VTI) kernel to estimate the background wavefield and the corresponding perturbation coefficients. The VTI extrapolation kernel is about one-fourth the cost of the transversely isotropic model with a tilt in the symmetry axis kernel. Thus, for a small symmetry axis tilt, the cost of migration using a first-order expansion can be reduced. The effectiveness of the approach was demonstrated on the Marmousi model.

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

Energy Technology Data Exchange (ETDEWEB)

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

2001-02-01

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

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

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.

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.

Contribution of higher order terms in the reductive perturbation theory, 2

International Nuclear Information System (INIS)

Ichikawa, Y.H.; Mitsuhashi, Teruo; Konno, Kimiaki.

1977-01-01

Contribution of higher order terms in the reductive perturbation theory has been investigated for nonlinear propagation of strongly dispersive ion plasma wave. The basic set of fluid equation is reduced to a coupled set of the nonlinear Schroedinger equation for the first order perturbed potential and a linear inhomogeneous equation for the second order perturbed potential. A steady state solution of the coupled set of equations has been solved analytically in the asymptotic limit of small wave number. (auth.)

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)

Systems of evolution equations and the singular perturbation method

International Nuclear Information System (INIS)

Mika, J.

Several fundamental theorems are presented important for the solution of linear evolution equations in the Banach space. The algorithm is deduced extending the solution of the system of singularly perturbed evolution equations into an asymptotic series with respect to a small positive parameter. The asymptotic convergence is shown of an approximate solution to the accurate solution. Singularly perturbed evolution equations of the resonance type were analysed. The special role is considered of the asymptotic equivalence of P1 equations obtained as the first order approximation if the spherical harmonics method is applied to the linear Boltzmann equation, and the diffusion equations of the linear transport theory where the small parameter approaches zero. (J.B.)

Optimized Perturbation Theory for Wave Functions of Quantum Systems

International Nuclear Information System (INIS)

Hatsuda, T.; Tanaka, T.; Kunihiro, T.

1997-01-01

The notion of the optimized perturbation, which has been successfully applied to energy eigenvalues, is generalized to treat wave functions of quantum systems. The key ingredient is to construct an envelope of a set of perturbative wave functions. This leads to a condition similar to that obtained from the principle of minimal sensitivity. Applications of the method to the quantum anharmonic oscillator and the double well potential show that uniformly valid wave functions with correct asymptotic behavior are obtained in the first-order optimized perturbation even for strong couplings. copyright 1997 The American Physical Society

Singularly perturbed Burger-Huxley equation: Analytical solution ...

African Journals Online (AJOL)

The work presented considers the initial boundary value problem for nonlinear singularly perturbed time dependent Burger- Huxley equation. The equation contains two terms with nonlinearities, the cubic term and the advection term. Generally, the severe difficulties of two types encounter in solving this problem. The first ...

Stability properties of solitary waves for fractional KdV and BBM equations

Science.gov (United States)

Angulo Pava, Jaime

2018-03-01

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

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.

Perturbations of the Friedmann universe

International Nuclear Information System (INIS)

Novello, M.; Salim, J.M.; Heintzmann, H.

1982-01-01

Correcting and extending previous work by Hawking (1966) and Olson (1976) the complete set of perturbation equations of a Friedmann Universe in the quasi-Maxwellian form is derived and analized. The formalism is then applied to scalar, vector and tensor perturbations of a phenomenological fluid, which is modelled such as to comprise shear and heat flux. Depending on the equation of state of the background it is found that there exist unstable (growing) modes of purely rotational character. It is further found that (to linear order at least) any vortex perturbation is equivalent to a certain heat flux vector. The equation for the gravitational waves are derived in a completely equivalent method as in case of the propagation, in a curved space-time, of electromagnetic waves in a plasma endowed with some definite constitutive relations. (Author) [pt

Collective behaviour of linear perturbation waves observed through the energy density spectrum

Energy Technology Data Exchange (ETDEWEB)

Scarsoglio, S [Department of Water Engineering, Politecnico di Torino (Italy); De Santi, F; Tordella, D, E-mail: stefania.scarsoglio@polito.it [Department of Aeronautics and Space Engineering, Politecnico di Torino (Italy)

2011-12-22

We consider the collective behaviour of small three-dimensional transient perturbations in sheared flows. In particular, we observe their varied life history through the temporal evolution of the amplification factor. The spectrum of wave vectors considered fills the range from the size of the external flow scale to the size of the very short dissipative waves. We observe that the amplification factor distribution is scale-invariant. In the condition we analyze, the system is subject to all the physical processes included in the linearized Navier-Stokes equations. With the exception of the nonlinear interaction, these features are the same as those characterizing the turbulent state. The linearized perturbative system offers a great variety of different transient behaviours associated to the parameter combination present in the initial conditions. For the energy spectrum computed by freezing each wave at the instant where its asymptotic condition is met, we ask whether this system is able to show a power-law scaling analogous to the Kolmogorov argument. At the moment, for at least two typical shear flows, the bluff-body wake and the plane Poiseuille flow, the answer is yes.

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.

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.

On Direct Transformation Approach to Asymptotical Analytical Solutions of Perturbed Partial Differential Equation

International Nuclear Information System (INIS)

Liu Hongzhun; Pan Zuliang; Li Peng

2006-01-01

In this article, we will derive an equality, where the Taylor series expansion around ε = 0 for any asymptotical analytical solution of the perturbed partial differential equation (PDE) with perturbing parameter ε must be admitted. By making use of the equality, we may obtain a transformation, which directly map the analytical solutions of a given unperturbed PDE to the asymptotical analytical solutions of the corresponding perturbed one. The notion of Lie-Baecklund symmetries is introduced in order to obtain more transformations. Hence, we can directly create more transformations in virtue of known Lie-Baecklund symmetries and recursion operators of corresponding unperturbed equation. The perturbed Burgers equation and the perturbed Korteweg-de Vries (KdV) equation are used as examples.

Exact non-linear equations for cosmological perturbations

Energy Technology Data Exchange (ETDEWEB)

Gong, Jinn-Ouk [Asia Pacific Center for Theoretical Physics, Pohang 37673 (Korea, Republic of); Hwang, Jai-chan [Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu 41566 (Korea, Republic of); Noh, Hyerim [Korea Astronomy and Space Science Institute, Daejeon 34055 (Korea, Republic of); Wu, David Chan Lon; Yoo, Jaiyul, E-mail: jinn-ouk.gong@apctp.org, E-mail: jchan@knu.ac.kr, E-mail: hr@kasi.re.kr, E-mail: clwu@physik.uzh.ch, E-mail: jyoo@physik.uzh.ch [Center for Theoretical Astrophysics and Cosmology, Institute for Computational Science, Universität Zürich, CH-8057 Zürich (Switzerland)

2017-10-01

We present a complete set of exact and fully non-linear equations describing all three types of cosmological perturbations—scalar, vector and tensor perturbations. We derive the equations in a thoroughly gauge-ready manner, so that any spatial and temporal gauge conditions can be employed. The equations are completely general without any physical restriction except that we assume a flat homogeneous and isotropic universe as a background. We also comment briefly on the application of our formulation to the non-expanding Minkowski background.

Structural stability and chaotic solutions of perturbed Benjamin-Ono equations

International Nuclear Information System (INIS)

Birnir, B.; Morrison, P.J.

1986-11-01

A method for proving chaos in partial differential equations is discussed and applied to the Benjamin-Ono equation subject to perturbations. The perturbations are of two types: one that corresponds to viscous dissipation, the so-called Burger's term, and one that involves the Hilbert transform and has been used to model Landau damping. The method proves chaos in the PDE by proving temporal chaos in its pole solutions. The spatial structure of the pole solutions remains intact, but their positions are chaotic in time. Melnikov's method is invoked to show this temporal chaos. It is discovered that the pole behavior is very sensitive to the Burger's perturbation, but is quite insensitive to the perturbation involving the Hilbert transform

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

International Nuclear Information System (INIS)

Guo Shimin; Wang Hongli; Mei Liquan

2012-01-01

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

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.)

Covariant perturbations of Schwarzschild black holes

International Nuclear Information System (INIS)

Clarkson, Chris A; Barrett, Richard K

2003-01-01

We present a new covariant and gauge-invariant perturbation formalism for dealing with spacetimes having spherical symmetry (or some preferred spatial direction) in the background, and apply it to the case of gravitational wave propagation in a Schwarzschild black-hole spacetime. The 1 + 3 covariant approach is extended to a '1 + 1 + 2 covariant sheet' formalism by introducing a radial unit vector in addition to the timelike congruence, and decomposing all covariant quantities with respect to this. The background Schwarzschild solution is discussed and a covariant characterization is given. We give the full first-order system of linearized 1 + 1 + 2 covariant equations, and we show how, by introducing (time and spherical) harmonic functions, these may be reduced to a system of first-order ordinary differential equations and algebraic constraints for the 1 + 1 + 2 variables which may be solved straightforwardly. We show how both odd- and even-parity perturbations may be unified by the discovery of a covariant, frame- and gauge-invariant, transverse-traceless tensor describing gravitational waves, which satisfies a covariant wave equation equivalent to the Regge-Wheeler equation for both even- and odd-parity perturbations. We show how the Zerilli equation may be derived from this tensor, and derive a similar transverse-traceless tensor equation equivalent to this equation. The so-called special quasinormal modes with purely imaginary frequency emerge naturally. The significance of the degrees of freedom in the choice of the two frame vectors is discussed, and we demonstrate that, for a certain frame choice, the underlying dynamics is governed purely by the Regge-Wheeler tensor. The two transverse-traceless Weyl tensors which carry the curvature of gravitational waves are discussed, and we give the closed system of four first-order ordinary differential equations describing their propagation. Finally, we consider the extension of this work to the study of

The two-fermion relativistic wave equations of Constraint Theory in the Pauli-Schroedinger form

International Nuclear Information System (INIS)

Mourad, J.; Sazdjian, H.

1994-01-01

The two-fermion relativistic wave equations of Constraint Theory are reduced, after expressing the components of the 4x4 matrix wave function in terms of one of the 2x2 components, to a single equation of the Pauli-Schroedinger type, valid for all sectors of quantum numbers. The potentials that are present belong to the general classes of scalar, pseudoscalar and vector interactions and are calculable in perturbation theory from Feynman diagrams. In the limit when one of the masses becomes infinite, the equation reduces to the two-component form of the one-particle Dirac equation with external static potentials. The Hamiltonian, to order 1/c 2 , reproduces most of the known theoretical results obtained by other methods. The gauge invariance of the wave equation is checked, to that order, in the case of QED. The role of the c.m. energy dependence of the relativistic interquark confining potential is emphasized and the structure of the Hamiltonian, to order 1/c 2 , corresponding to confining scalar potentials, is displayed. (authors). 32 refs., 2 figs

Homoclinic tubes and chaos in perturbed sine-Gordon equation

International Nuclear Information System (INIS)

Li, Y. Charles

2004-01-01

Sine-Gordon equation under a quasi-periodic perturbation or a chaotic perturbation is studied. Existence of a homoclinic tube is proved. Established are chaos associated with the homoclinic tube, and 'chaos cascade' referring to the embeddings of smaller scale chaos in larger scale chaos

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

A Variational Approach to Perturbed Discrete Anisotropic Equations

Directory of Open Access Journals (Sweden)

Amjad Salari

2016-01-01

Full Text Available We continue the study of discrete anisotropic equations and we will provide new multiplicity results of the solutions for a discrete anisotropic equation. We investigate the existence of infinitely many solutions for a perturbed discrete anisotropic boundary value problem. The approach is based on variational methods and critical point theory.

Equation-of-motion coupled cluster perturbation theory revisited

DEFF Research Database (Denmark)

Eriksen, Janus Juul; Jørgensen, Poul; Olsen, Jeppe

2014-01-01

The equation-of-motion coupled cluster (EOM-CC) framework has been used for deriving a novel series of perturbative corrections to the coupled cluster singles and doubles energy that formally con- verges towards the full configuration interaction energy limit. The series is based on a Møller-Ples......-Plesset partitioning of the Hamiltonian and thus size extensive at any order in the perturbation, thereby rem- edying the major deficiency inherent to previous perturbation series based on the EOM-CC ansatz. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4873138]...

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

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.)

Acoustic wavefield evolution as a function of source location perturbation

KAUST Repository

Alkhalifah, Tariq Ali

2010-12-01

The wavefield is typically simulated for seismic exploration applications through solving the wave equation for a specific seismic source location. The direct relation between the form (or shape) of the wavefield and the source location can provide insights useful for velocity estimation and interpolation. As a result, I derive partial differential equations that relate changes in the wavefield shape to perturbations in the source location, especially along the Earth\\'s surface. These partial differential equations have the same structure as the wave equation with a source function that depends on the background (original source) wavefield. The similarity in form implies that we can use familiar numerical methods to solve the perturbation equations, including finite difference and downward continuation. In fact, we can use the same Green\\'s function to solve the wave equation and its source perturbations by simply incorporating source functions derived from the background field. The solutions of the perturbation equations represent the coefficients of a Taylor\\'s series type expansion of the wavefield as a function of source location. As a result, we can speed up the wavefield calculation as we approximate the wavefield shape for sources in the vicinity of the original source. The new formula introduces changes to the background wavefield only in the presence of lateral velocity variation or in general terms velocity variations in the perturbation direction. The approach is demonstrated on the smoothed Marmousi model.

Dynamic behaviors for a perturbed nonlinear Schrödinger equation with the power-law nonlinearity in a non-Kerr medium

Science.gov (United States)

Chai, Jun; Tian, Bo; Zhen, Hui-Ling; Sun, Wen-Rong; Liu, De-Yin

2017-04-01

Effects of quantic nonlinearity on the propagation of the ultrashort optical pulses in a non-Kerr medium, like an optical fiber, can be described by a perturbed nonlinear Schrödinger equation with the power law nonlinearity, which is studied in this paper from a planar-dynamic-system view point. We obtain the equivalent two-dimensional planar dynamic system of such an equation, for which, according to the bifurcation theory and qualitative theory, phase portraits are given. Through the analysis of those phase portraits, we present the relations among the Hamiltonian, orbits of the dynamic system and types of the analytic solutions. Analytic expressions of the periodic-wave solutions, kink- and bell-shaped solitary-wave solutions are derived, and we find that the periodic-wave solutions can be reduced to the kink- and bell-shaped solitary-wave solutions.

Three-Dimensional Coupled NLS Equations for Envelope Gravity Solitary Waves in Baroclinic Atmosphere and Modulational Instability

Directory of Open Access Journals (Sweden)

Baojun Zhao

2018-01-01

Full Text Available Envelope gravity solitary waves are an important research hot spot in the field of solitary wave. And the weakly nonlinear model equations system is a part of the research of envelope gravity solitary waves. Because of the lack of technology and theory, previous studies tried hard to reduce the variable numbers and constructed the two-dimensional model in barotropic atmosphere and could only describe the propagation feature in a direction. But for the propagation of envelope gravity solitary waves in real ocean ridges and atmospheric mountains, the three-dimensional model is more appropriate. Meanwhile, the baroclinic problem of atmosphere is also an inevitable topic. In the paper, the three-dimensional coupled nonlinear Schrödinger (CNLS equations are presented to describe the evolution of envelope gravity solitary waves in baroclinic atmosphere, which are derived from the basic dynamic equations by employing perturbation and multiscale methods. The model overcomes two disadvantages: (1 baroclinic problem and (2 propagation path problem. Then, based on trial function method, we deduce the solution of the CNLS equations. Finally, modulational instability of wave trains is also discussed.

On some perturbation techniques for quasi-linear parabolic equations

Directory of Open Access Journals (Sweden)

Igor Malyshev

1990-01-01

Full Text Available We study a nonhomogeneous quasi-linear parabolic equation and introduce a method that allows us to find the solution of a nonlinear boundary value problem in “explicit” form. This task is accomplished by perturbing the original equation with a source function, which is then found as a solution of some nonlinear operator equation.

Green's function method for perturbed Korteweg-de Vries equation

International Nuclear Information System (INIS)

Cai Hao; Huang Nianning

2003-01-01

The x-derivatives of squared Jost solution are the eigenfunctions with the zero eigenvalue of the linearized equation derived from the perturbed Korteweg-de Vries equation. A method similar to Green's function formalism is introduced to show the completeness of the squared Jost solutions in multi-soliton cases. It is not related to Lax equations directly, and thus it is beneficial to deal with the nonlinear equations with complicated Lax pair

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)

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)

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)

Acoustic anisotropic wavefields through perturbation theory

KAUST Repository

Alkhalifah, Tariq Ali

2013-01-01

these restrictions are the inability to handle media with η<0 and the presence of shear-wave artifacts in the solution. Both limitations do not exist in the solution of the elliptical anisotropic acoustic wave equation. Using perturbation theory in developing

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

Science.gov (United States)

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

2018-02-01

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

Cosmological Perturbation Theory Using the Schrödinger Equation

Science.gov (United States)

Szapudi, István; Kaiser, Nick

2003-01-01

We introduce the theory of nonlinear cosmological perturbations using the correspondence limit of the Schrödinger equation. The resulting formalism is equivalent to using the collisionless Boltzmann (or Vlasov) equations, which remain valid during the whole evolution, even after shell crossing. Other formulations of perturbation theory explicitly break down at shell crossing, e.g., Eulerean perturbation theory, which describes gravitational collapse in the fluid limit. This Letter lays the groundwork by introducing the new formalism, calculating the perturbation theory kernels that form the basis of all subsequent calculations. We also establish the connection with conventional perturbation theories, by showing that third-order tree-level results, such as bispectrum, skewness, cumulant correlators, and three-point function, are exactly reproduced in the appropriate expansion of our results. We explicitly show that cumulants up to N=5 predicted by Eulerian perturbation theory for the dark matter field δ are exactly recovered in the corresponding limit. A logarithmic mapping of the field naturally arises in the Schrödinger context, which means that tree-level perturbation theory translates into (possibly incomplete) loop corrections for the conventional perturbation theory. We show that the first loop correction for the variance is σ2=σ2L+(-1.14- n)σ4L for a field with spectral index n. This yields 1.86 and 0.86 for n=-3 and -2, respectively, to be compared with the exact loop order corrections 1.82 and 0.88. Thus, our tree-level theory recovers the dominant part of first-order loop corrections of the conventional theory, while including (partial) loop corrections to infinite order in terms of δ.

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.

Motions in a Bose condensate: X. New results on stability of axisymmetric solitary waves of the Gross-Pitaevskii equation

OpenAIRE

Berloff, Natalia G.; Roberts, Paul H.

2004-01-01

The stability of the axisymmetric solitary waves of the Gross-Pitaevskii (GP) equation is investigated. The Implicitly Restarted Arnoldi Method for banded matrices with shift-invert was used to solve the linearised spectral stability problem. The rarefaction solitary waves on the upper branch of the Jones-Roberts dispersion curve are shown to be unstable to axisymmetric infinitesimal perturbations, whereas the solitary waves on the lower branch and all two-dimensional solitary waves are linea...

Linear perturbation growth at the trailing edge of a rarefaction wave

International Nuclear Information System (INIS)

Wouchuk, J.G.; Carretero, R.

2003-01-01

An analytic model for the perturbation growth inside a rarefaction wave is presented. The objective of the work is to calculate the growth of the perturbations at the trailing edge of a simple expanding wave in planar geometry. Previous numerical and analytical works have shown that the ripples at the rarefaction tail exhibit linear growth asymptotically in time [Yang et al., Phys. Fluids 6, 1856 (1994), A. Velikovich and L. Phillips, ibid. 8, 1107 (1996)]. However, closed expressions for the asymptotic value of the perturbed velocity of the trailing edge have not been reported before, except for very weak rarefactions. Explicit analytic solutions for the perturbations growing at the rarefaction trailing edge as a function of time and also for the asymptotic perturbed velocity are given, for fluids with γ<3. The limits of weak and strong rarefactions are considered and the corresponding scaling laws are given. A semi-qualitative discussion of the late time linear growth at the trailing edge ripple is presented and it is seen that the lateral mass flow induced by the sound wave fluctuations is solely responsible for that behavior. Only the rarefactions generated after the interaction of a shock wave with a contact discontinuity are considered

Application of functional analysis to perturbation theory of differential equations. [nonlinear perturbation of the harmonic oscillator

Science.gov (United States)

Bogdan, V. M.; Bond, V. B.

1980-01-01

The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.

Solving ground eigenvalue and eigenfunction of spheroidal wave equation at low frequency by supersymmetric quantum mechanics method

Institute of Scientific and Technical Information of China (English)

Tang Wen-Lin; Tian Gui-Hua

2011-01-01

The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eigenvalue and the ground eigenfunction of the angular spheroidal wave equation at low frequency in a series form. Using this approach, the numerical determinations of the ground eigenvalue and the ground eigenfunction for small complex frequencies are also obtained.

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.

Exact cosmological solutions of Einstein-Maxwell equations as perturbations of the Bertotti-Robinson model

International Nuclear Information System (INIS)

Portugal, R.; Soares, I.D.

1985-01-01

Two new classes of spatially homogeneous cosmological solutions of Einstein-Maxwell equations are obtained by considering a class of exact perturbations of the static Bertotti-Robinson (BR) model. The BR solution is shown to be unstable under these perturbations, being perturbed into exact cosmological solutions with perfect fluid (equations of state p = lambda rho, O [pt

Bifurcations of nonlinear ion acoustic travelling waves in the frame of a Zakharov-Kuznetsov equation in magnetized plasma with a kappa distributed electron

International Nuclear Information System (INIS)

Kumar Samanta, Utpal; Saha, Asit; Chatterjee, Prasanta

2013-01-01

Bifurcations of nonlinear propagation of ion acoustic waves (IAWs) in a magnetized plasma whose constituents are cold ions and kappa distributed electron are investigated using a two component plasma model. The standard reductive perturbation technique is used to derive the Zakharov-Kuznetsov (ZK) equation for IAWs. By using the bifurcation theory of planar dynamical systems to this ZK equation, the existence of solitary wave solutions and periodic travelling wave solutions is established. All exact explicit solutions of these travelling waves are determined. The results may have relevance in dense space plasmas

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

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

Directory of Open Access Journals (Sweden)

M. Arshad

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

A perturbational h4 exponential finite difference scheme for the convective diffusion equation

International Nuclear Information System (INIS)

Chen, G.Q.; Gao, Z.; Yang, Z.F.

1993-01-01

A perturbational h 4 compact exponential finite difference scheme with diagonally dominant coefficient matrix and upwind effect is developed for the convective diffusion equation. Perturbations of second order are exerted on the convective coefficients and source term of an h 2 exponential finite difference scheme proposed in this paper based on a transformation to eliminate the upwind effect of the convective diffusion equation. Four numerical examples including one- to three-dimensional model equations of fluid flow and a problem of natural convective heat transfer are given to illustrate the excellent behavior of the present exponential schemes. Besides, the h 4 accuracy of the perturbational scheme is verified using double precision arithmetic

Scattering of Ricci scalar perturbations from Schwarzschild black holes in modified gravity

Energy Technology Data Exchange (ETDEWEB)

Sibandze, Dan B.; Goswami, Rituparno; Maharaj, Sunil D.; Nzioki, Anne Marie [University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics Statistics and Computer Science, Private Bag X54001, Durban (South Africa); Dunsby, Peter K.S. [University of Cape Town, Department of Mathematics and Applied Mathematics and ACGC, Cape Town (South Africa)

2017-06-15

It has already been shown that the gravitational waves emitted from a Schwarzschild black hole in f(R) gravity have no signatures of the modification of gravity from General Relativity, as the Regge-Wheeler equation remains invariant. In this paper we consider the perturbations of Ricci scalar in a vacuum Schwarzschild spacetime, which is unique to higher order theories of gravity and is absent in General Relativity. We show that the equation that governs these perturbations can be reduced to a Volterra integral equation. We explicitly calculate the reflection coefficients for the Ricci scalar perturbations, when they are scattered by the black hole potential barrier. Our analysis shows that a larger fraction of these Ricci scalar waves are reflected compared to the gravitational waves. This may provide a novel observational signature for fourth order gravity. (orig.)

Theory of Perturbed Equilibria for Solving the Grad-Shafranov Equation

International Nuclear Information System (INIS)

Pletzer, A.; Zakharov, L.E.

1999-01-01

The theory of perturbed magnetohydrodynamic equilibria is presented for different formulations of the tokamak equilibrium problem. For numerical codes, it gives an explicit Newton scheme for solving the Grad-Shafranov equation subject to different constraints. The problem of stability of axisymmetric modes is shown to be a particular case of the equilibrium perturbation theory

Gravitational perturbations of the Schwarzschild spacetime: A practical covariant and gauge-invariant formalism

International Nuclear Information System (INIS)

Martel, Karl; Poisson, Eric

2005-01-01

We present a formalism to study the metric perturbations of the Schwarzschild spacetime. The formalism is gauge invariant, and it is also covariant under two-dimensional coordinate transformations that leave the angular coordinates unchanged. The formalism is applied to the typical problem of calculating the gravitational waves produced by material sources moving in the Schwarzschild spacetime. We examine the radiation escaping to future null infinity as well as the radiation crossing the event horizon. The waveforms, the energy radiated, and the angular-momentum radiated can all be expressed in terms of two gauge-invariant scalar functions that satisfy one-dimensional wave equations. The first is the Zerilli-Moncrief function, which satisfies the Zerilli equation, and which represents the even-parity sector of the perturbation. The second is the Cunningham-Price-Moncrief function, which satisfies the Regge-Wheeler equation, and which represents the odd-parity sector of the perturbation. The covariant forms of these wave equations are presented here, complete with covariant source terms that are derived from the stress-energy tensor of the matter responsible for the perturbation

Perturbative approach to non-Markovian stochastic Schroedinger equations

International Nuclear Information System (INIS)

Gambetta, Jay; Wiseman, H.M.

2002-01-01

In this paper we present a perturbative procedure that allows one to numerically solve diffusive non-Markovian stochastic Schroedinger equations, for a wide range of memory functions. To illustrate this procedure numerical results are presented for a classically driven two-level atom immersed in an environment with a simple memory function. It is observed that as the order of the perturbation is increased the numerical results for the ensemble average state ρ red (t) approach the exact reduced state found via Imamog-barlu ' s enlarged system method [Phys. Rev. A 50, 3650 (1994)

Fourth-order Perturbed Eigenvalue Equation for Stepwise Damage Detection of Aeroplane Wing

Directory of Open Access Journals (Sweden)

Wong Chun Nam

2016-01-01

Full Text Available Perturbed eigenvalue equations up to fourth-order are established to detect structural damage in aeroplane wing. Complete set of perturbation terms including orthogonal and non-orthogonal coefficients are computed using perturbed eigenvalue and orthonormal equations. Then the perturbed eigenparameters are optimized using BFGS approach. Finite element model with small to large stepwise damage is used to represent actual aeroplane wing. In small damaged level, termination number is the same for both approaches, while rms errors and termination d-norms are very close. For medium damaged level, termination number is larger for third-order perturbation with lower d-norm and smaller rms error. In large damaged level, termination number is much larger for third-order perturbation with same d-norm and larger rms error. These trends are more significant as the damaged level increases. As the stepwise damage effect increases with damage level, the increase in stepwise effect leads to the increase in model order. Hence, fourth-order perturbation is more accurate to estimate the model solution.

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

Numerical Integration of a Class of Singularly Perturbed Delay Differential Equations with Small Shift

Directory of Open Access Journals (Sweden)

Gemechis File

2012-01-01

Full Text Available We have presented a numerical integration method to solve a class of singularly perturbed delay differential equations with small shift. First, we have replaced the second-order singularly perturbed delay differential equation by an asymptotically equivalent first-order delay differential equation. Then, Simpson’s rule and linear interpolation are employed to get the three-term recurrence relation which is solved easily by discrete invariant imbedding algorithm. The method is demonstrated by implementing it on several linear and nonlinear model examples by taking various values for the delay parameter and the perturbation parameter .

Motions in a Bose condensate: X. New results on the stability of axisymmetric solitary waves of the Gross-Pitaevskii equation

International Nuclear Information System (INIS)

Berloff, Natalia G; Roberts, Paul H

2004-01-01

The stability of the axisymmetric solitary waves of the Gross-Pitaevskii (GP) equation is investigated. The implicitly restarted Arnoldi method for banded matrices with shift-invert is used to solve the linearized spectral stability problem. The rarefaction solitary waves on the upper branch of the Jones-Roberts dispersion curve are shown to be unstable to axisymmetric infinitesimal perturbations, whereas the solitary waves on the lower branch and all two-dimensional solitary waves are linearly stable. The growth rates of the instabilities on the upper branch are so small that an arbitrarily specified initial perturbation of a rarefaction wave at first usually evolves towards the upper branch as it acoustically radiates away its excess energy. This is demonstrated through numerical integrations of the GP equation starting from an initial state consisting of an unstable rarefaction wave and random non-axisymmetric noise. The resulting solution evolves towards, and remains for a significant time in the vicinity of, an unperturbed unstable rarefaction wave. It is shown however that, ultimately (or for an initial state extremely close to the upper branch), the solution evolves onto the lower branch or is completely dissipated as sound. It is shown how density depletions in uniform and trapped condensates can generate rarefaction waves, and a simple method is suggested by which such waves can be created in the laboratory

Motions in a Bose condensate: X. New results on the stability of axisymmetric solitary waves of the Gross-Pitaevskii equation

Energy Technology Data Exchange (ETDEWEB)

Berloff, Natalia G [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA (United Kingdom); Roberts, Paul H [Department of Mathematics, University of California, Los Angeles, CA, 90095 (United States)

2004-11-26

The stability of the axisymmetric solitary waves of the Gross-Pitaevskii (GP) equation is investigated. The implicitly restarted Arnoldi method for banded matrices with shift-invert is used to solve the linearized spectral stability problem. The rarefaction solitary waves on the upper branch of the Jones-Roberts dispersion curve are shown to be unstable to axisymmetric infinitesimal perturbations, whereas the solitary waves on the lower branch and all two-dimensional solitary waves are linearly stable. The growth rates of the instabilities on the upper branch are so small that an arbitrarily specified initial perturbation of a rarefaction wave at first usually evolves towards the upper branch as it acoustically radiates away its excess energy. This is demonstrated through numerical integrations of the GP equation starting from an initial state consisting of an unstable rarefaction wave and random non-axisymmetric noise. The resulting solution evolves towards, and remains for a significant time in the vicinity of, an unperturbed unstable rarefaction wave. It is shown however that, ultimately (or for an initial state extremely close to the upper branch), the solution evolves onto the lower branch or is completely dissipated as sound. It is shown how density depletions in uniform and trapped condensates can generate rarefaction waves, and a simple method is suggested by which such waves can be created in the laboratory.

Difference scheme for a singularly perturbed parabolic convection-diffusion equation in the presence of perturbations

Science.gov (United States)

Shishkin, G. I.

2015-11-01

An initial-boundary value problem is considered for a singularly perturbed parabolic convection-diffusion equation with a perturbation parameter ɛ (ɛ ∈ (0, 1]) multiplying the highest order derivative. The stability of a standard difference scheme based on monotone approximations of the problem on a uniform mesh is analyzed, and the behavior of discrete solutions in the presence of perturbations is examined. The scheme does not converge ɛ-uniformly in the maximum norm as the number of its grid nodes is increased. When the solution of the difference scheme converges, which occurs if N -1 ≪ ɛ and N -1 0 ≪ 1, where N and N 0 are the numbers of grid intervals in x and t, respectively, the scheme is not ɛ-uniformly well conditioned or stable to data perturbations in the grid problem and to computer perturbations. For the standard difference scheme in the presence of data perturbations in the grid problem and/or computer perturbations, conditions on the "parameters" of the difference scheme and of the computer (namely, on ɛ, N, N 0, admissible data perturbations in the grid problem, and admissible computer perturbations) are obtained that ensure the convergence of the perturbed solutions. Additionally, the conditions are obtained under which the perturbed numerical solution has the same order of convergence as the solution of the unperturbed standard difference scheme.

Perturbations of linear delay differential equations at the verge of instability.

Science.gov (United States)

Lingala, N; Namachchivaya, N Sri

2016-06-01

The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. This paper considers linear DDEs that are on the verge of instability, i.e., a pair of roots of the characteristic equation lies on the imaginary axis of the complex plane and all other roots have negative real parts. It is shown that when small noise perturbations are present, the probability distribution of the dynamics can be approximated by the probability distribution of a certain one-dimensional stochastic differential equation (SDE) without delay. This is advantageous because equations without delay are easier to simulate and one-dimensional SDEs are analytically tractable. When the perturbations are also linear, it is shown that the stability depends on a specific complex number. The theory is applied to study oscillators with delayed feedback. Some errors in other articles that use multiscale approach are pointed out.

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

On the comparison of perturbation-iteration algorithm and residual power series method to solve fractional Zakharov-Kuznetsov equation

Science.gov (United States)

Şenol, Mehmet; Alquran, Marwan; Kasmaei, Hamed Daei

2018-06-01

In this paper, we present analytic-approximate solution of time-fractional Zakharov-Kuznetsov equation. This model demonstrates the behavior of weakly nonlinear ion acoustic waves in a plasma bearing cold ions and hot isothermal electrons in the presence of a uniform magnetic field. Basic definitions of fractional derivatives are described in the Caputo sense. Perturbation-iteration algorithm (PIA) and residual power series method (RPSM) are applied to solve this equation with success. The convergence analysis is also presented for both methods. Numerical results are given and then they are compared with the exact solutions. Comparison of the results reveal that both methods are competitive, powerful, reliable, simple to use and ready to apply to wide range of fractional partial differential equations.

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.

A global numerical solution of the radial Schroedinger equation by second-order perturbation theory

International Nuclear Information System (INIS)

Adam, G.

1979-01-01

A global numerical method, which uses second-order perturbation theory, is described for the solution of the radial Schroedinger equation. The perturbative numerical (PN) solution is derived in two stages: first, the original potential is approximated by a piecewise continuous parabolic function, and second, the resulting Schroedinger equation is solved on each integration step by second-order perturbation theory, starting with a step function reference approximation for the parabolic potential. We get a manageable PN algorithm, which shows an order of accuracy equal to six in the solution of the original Schroedinger equation, and is very stable against round off errors. (author)

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.

Acoustic wavefield evolution as a function of source location perturbation

KAUST Repository

Alkhalifah, Tariq Ali

2010-01-01

differential equations have the same structure as the wave equation with a source function that depends on the background (original source) wavefield. The similarity in form implies that we can use familiar numerical methods to solve the perturbation equations

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.

Gravitational Wave in Linear General Relativity

Science.gov (United States)

Cubillos, D. J.

2017-07-01

General relativity is the best theory currently available to describe the interaction due to gravity. Within Albert Einstein's field equations this interaction is described by means of the spatiotemporal curvature generated by the matter-energy content in the universe. Weyl worked on the existence of perturbations of the curvature of space-time that propagate at the speed of light, which are known as Gravitational Waves, obtained to a first approximation through the linearization of the field equations of Einstein. Weyl's solution consists of taking the field equations in a vacuum and disturbing the metric, using the Minkowski metric slightly perturbed by a factor ɛ greater than zero but much smaller than one. If the feedback effect of the field is neglected, it can be considered as a weak field solution. After introducing the disturbed metric and ignoring ɛ terms of order greater than one, we can find the linearized field equations in terms of the perturbation, which can then be expressed in terms of the Dalambertian operator of the perturbation equalized to zero. This is analogous to the linear wave equation in classical mechanics, which can be interpreted by saying that gravitational effects propagate as waves at the speed of light. In addition to this, by studying the motion of a particle affected by this perturbation through the geodesic equation can show the transversal character of the gravitational wave and its two possible states of polarization. It can be shown that the energy carried by the wave is of the order of 1/c5 where c is the speed of light, which explains that its effects on matter are very small and very difficult to detect.

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

Separate P‐ and SV‐wave equations for VTI media

KAUST Repository

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

2011-01-01

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

Automatic Wave Equation Migration Velocity Analysis by Focusing Subsurface Virtual Sources

KAUST Repository

Sun, Bingbing

2017-11-03

Macro velocity model building is important for subsequent pre-stack depth migration and full waveform inversion. Wave equation migration velocity analysis (WEMVA) utilizes the band-limited waveform to invert for the velocity. Normally, inversion would be implemented by focusing the subsurface offset common image gathers (SOCIGs). We re-examine this concept with a different perspective: In subsurface offset domain, using extended Born modeling, the recorded data can be considered as invariant with respect to the perturbation of the position of the virtual sources and velocity at the same time. A linear system connecting the perturbation of the position of those virtual sources and velocity is derived and solved subsequently by Conjugate Gradient method. In theory, the perturbation of the position of the virtual sources is given by the Rytov approximation. Thus, compared to the Born approximation, it relaxes the dependency on amplitude and makes the proposed method more applicable for real data. We demonstrate the effectiveness of the approach by applying the proposed method on both isotropic and anisotropic VTI synthetic data. A real dataset example verifies the robustness of the proposed method.

Automatic Wave Equation Migration Velocity Analysis by Focusing Subsurface Virtual Sources

KAUST Repository

Sun, Bingbing; Alkhalifah, Tariq Ali

2017-01-01

Macro velocity model building is important for subsequent pre-stack depth migration and full waveform inversion. Wave equation migration velocity analysis (WEMVA) utilizes the band-limited waveform to invert for the velocity. Normally, inversion would be implemented by focusing the subsurface offset common image gathers (SOCIGs). We re-examine this concept with a different perspective: In subsurface offset domain, using extended Born modeling, the recorded data can be considered as invariant with respect to the perturbation of the position of the virtual sources and velocity at the same time. A linear system connecting the perturbation of the position of those virtual sources and velocity is derived and solved subsequently by Conjugate Gradient method. In theory, the perturbation of the position of the virtual sources is given by the Rytov approximation. Thus, compared to the Born approximation, it relaxes the dependency on amplitude and makes the proposed method more applicable for real data. We demonstrate the effectiveness of the approach by applying the proposed method on both isotropic and anisotropic VTI synthetic data. A real dataset example verifies the robustness of the proposed method.

Perturbation analysis of a parametrically changed sine-Gordon equation

DEFF Research Database (Denmark)

Sakai, S.; Samuelsen, Mogens Rugholm; Olsen, O. H.

1987-01-01

A long Josephson junction with a spatially varying inductance is a physical manifestation of a modified sine-Gordon equation with parametric perturbation. Soliton propagation in such Josephson junctions is discussed. First, for an adiabatic model where the inductance changes smoothly compared...

Study of Perturbations on High Mach Number Blast Waves in Various Gasses

Science.gov (United States)

Edens, A.; Adams, R.; Rambo, P.; Shores, J.; Smith, I.; Atherton, B.; Ditmire, T.

2006-10-01

We have performed a series of experiments examining the properties of high Mach number blast waves. Experiments were conducted on the Z-Beamlet^1 laser at Sandia National Laboratories. We created blast waves in the laboratory by using 10 J- 1000 J laser pulses to illuminate millimeter scale solid targets immersed in gas. Our experiments studied the validity of theories forwarded by Vishniac and Ryu^2-4 to explain the dynamics of perturbations on astrophysical blast waves. These experiments consisted of an examination of the evolution of perturbations of known primary mode number induced on the surface of blast waves by means of regularly spaced wire arrays. The temporal evolution of the amplitude of the induced perturbations relative to the mean radius of the blast wave was fit to a power law in time. Measurements were taken for a number of different mode numbers and background gasses and the results show qualitative agreement with previously published theories for the hydrodynamics of thin shell blast wave. The results for perturbations on nitrogen gas have been recently published^5. .^1 P. K. Rambo, I. C. Smith, J. L. Porter, et al., Applied Optics 44, 2421 (2005). ^2 D. Ryu and E. T. Vishniac, Astrophysical Journal 313, 820 (1987). ^3 D. Ryu and E. T. Vishniac, Astrophysical Journal 368, 411 (1991). ^4 E. T. Vishniac, Astrophysical Journal 274, 152 (1983). ^5 A. D. Edens, T. Ditmire, J. F. Hansen, et al., Physical Review Letters 95 (2005).

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

International Nuclear Information System (INIS)

Ablowitz, Mark J; Curtis, Christopher W

2011-01-01

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

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

Science.gov (United States)

Ablowitz, Mark J.; Curtis, Christopher W.

2011-05-01

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

A hybrid perturbation-Galerkin technique for partial differential equations

Science.gov (United States)

Geer, James F.; Anderson, Carl M.

1990-01-01

A two-step hybrid perturbation-Galerkin technique for improving the usefulness of perturbation solutions to partial differential equations which contain a parameter is presented and discussed. In the first step of the method, the leading terms in the asymptotic expansion(s) of the solution about one or more values of the perturbation parameter are obtained using standard perturbation methods. In the second step, the perturbation functions obtained in the first step are used as trial functions in a Bubnov-Galerkin approximation. This semi-analytical, semi-numerical hybrid technique appears to overcome some of the drawbacks of the perturbation and Galerkin methods when they are applied by themselves, while combining some of the good features of each. The technique is illustrated first by a simple example. It is then applied to the problem of determining the flow of a slightly compressible fluid past a circular cylinder and to the problem of determining the shape of a free surface due to a sink above the surface. Solutions obtained by the hybrid method are compared with other approximate solutions, and its possible application to certain problems associated with domain decomposition is discussed.

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

Noise-induced perturbations of dispersion-managed solitons

International Nuclear Information System (INIS)

Li, Jinglai; Spiller, Elaine; Biondini, Gino

2007-01-01

We study noise-induced perturbations of dispersion-managed solitons. We do so by first developing soliton perturbation theory for the dispersion-managed nonlinear Schroedinger (DMNLS) equation, which governs the long-term behavior of optical fiber transmission systems and certain kinds of femtosecond lasers. We show that the eigenmodes and generalized eigenmodes of the linearized DMNLS equation around traveling-wave solutions can be generated from the invariances of the DMNLS equations, we quantify the perturbation-induced parameter changes of the solution in terms of the eigenmodes and the adjoint eigenmodes, and we obtain evolution equations for the solution parameters. We then apply these results to guide importance-sampled Monte Carlo (MC) simulations and reconstruct the probability density functions of the solution parameters under the effect of noise, and we compare with standard MC simulations of the unaveraged system. The comparison further validates the use of the DMNLS equation as a model for dispersion-managed systems

Meson spectra from two-body dirac equations with minimal interactions

International Nuclear Information System (INIS)

Crater, H.W.; Becker, R.L.; Wong, C.Y.

1991-01-01

Many authors have used two-body relativistic wave equations with spin in nonperturbative numerical quark model calculations of the meson spectrum. Usually, they adopt a truncation of the Bethe-Salpeter equation of QED and/or scalar. QED and replace the static Coulomb interactions of those field theories with a semiphenomenological Q bar Q potential whose insertion in the Breit terms give the corresponding spin corrections. However, the successes of these wave equations in QED have invariably depended on perturbative treatment of the terms in each beyond the Coulomb terms. There have been no successful nonperturbative numerical test of two-body quantum wave equations in QED, because in most equations the effective potentials beyond the Coulomb are singular and can only be treated perturbatively. This is a glaring omission that we rectify here for the case of the two-body Dirac equations of constraint dynamics. We show in this paper that a nonperturbative numerical treatment of these equations for QED yields the same spectral results as a perturbative treatment of them which in turn agrees with the standard spectral results for positronium and muonium. This establishes that the vector and scalar interaction structures of our equations accurately incorporate field theoretic interactions in a bone fide relativistic wave equation. The last portion of this work will report recent quark model calculations using these equations with the Adler-Piran static Q bar Q potential

High-power millimeter-wave mode converters in overmoded circular waveguides using periodic wall perturbations

International Nuclear Information System (INIS)

Thumm, M.

1984-07-01

This work reports on measurements and calculations (coupled mode equations) on the conversion of circular elecric TEsub(0n) gyrotron mode compositions (TE 01 to TE 04 ) at 28 and 70 GHz to the linearly polarized TE 11 mode by means of a mode converter system using periodic waveguide wall perturbations. Mode transducers with axisymmetric radius perturbations transform the TEsub(0n) gyrotron mode mixture to the more convenient TE 01 mode for long-distance transmission through overmoded waveguides. Proper matching of the phase differences between the TEsub(0n) modes and of lengths and perturbation amplitudes of the several converter sections is required. A mode converter with constant diameter and periodically perturbed curvature transfers the unpolarized TE 01 mode into the TE 11 mode which produces an almost linearly polarized millimeter-wave beam needed for efficient electron cyclotron heating (ECRH) of plasmas in thermonuclear fusion devices. The experimentally determined TEsub(0n)-to-TE 01 conversion efficiency is (98+-1)% at 28 and 70 GHz (99% predicted) while the TE 01 -to-TE 11 converter has a (96+-2)% conversion efficiency at 28 GHz (95% predicted) and (94+-2)% at 70 GHz (93% predicted); ohmic losses are included. (orig./AH)

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.

Correlations between chaos in a perturbed sine-Gordon equation and a truncated model system

International Nuclear Information System (INIS)

Bishop, A.R.; Flesch, R.; Forests, M.G.; Overman, E.A.

1990-01-01

The purpose of this paper is to present a first step toward providing coordinates and associated dynamics for low-dimensional attractors in nearly integrable partial differential equations (pdes), in particular, where the truncated system reflects salient geometric properties of the pde. This is achieved by correlating: (1) numerical results on the bifurcations to temporal chaos with spatial coherence of the damped, periodically forced sine-Gordon equation with periodic boundary conditions; (2) an interpretation of the spatial and temporal bifurcation structures of this perturbed integrable system with regard to the exact structure of the sine-Gordon phase space; (3) a model dynamical systems problem, which is itself a perturbed integrable Hamiltonian system, derived from the perturbed sine-Gordon equation by a finite mode Fourier truncation in the nonlinear Schroedinger limit; and (4) the bifurcations to chaos in the truncated phase space. In particular, a potential source of chaos in both the pde and the model ordinary differential equation systems is focused on: the existence of homoclinic orbits in the unperturbed integrable phase space and their continuation in the perturbed problem. The evidence presented here supports the thesis that the chaotic attractors of the weakly perturbed periodic sine-Gordon system consists of low-dimensional metastable attacking states together with intermediate states that are O(1) unstable and correspond to homoclinic states in the integrable phase space. It is surmised that the chaotic dynamics on these attractors is due to the perturbation of these homocline integrable configurations

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...

Numerical solution of Euler's equation by perturbed functionals

Science.gov (United States)

Dey, S. K.

1985-01-01

A perturbed functional iteration has been developed to solve nonlinear systems. It adds at each iteration level, unique perturbation parameters to nonlinear Gauss-Seidel iterates which enhances its convergence properties. As convergence is approached these parameters are damped out. Local linearization along the diagonal has been used to compute these parameters. The method requires no computation of Jacobian or factorization of matrices. Analysis of convergence depends on properties of certain contraction-type mappings, known as D-mappings. In this article, application of this method to solve an implicit finite difference approximation of Euler's equation is studied. Some representative results for the well known shock tube problem and compressible flows in a nozzle are given.

A perturbation-based model for rectifier circuits

Directory of Open Access Journals (Sweden)

Vipin B. Vats

2006-01-01

Full Text Available A perturbation-theoretic analysis of rectifier circuits is presented. The governing differential equation of the half-wave rectifier with capacitor filter is analyzed by expanding the output voltage as a Taylor series with respect to an artificially introduced parameter in the nonlinearity of the diode characteristic as is done in quantum theory. The perturbation parameter introduced in the analysis is independent of the circuit components as compared to the method presented by multiple scales. The various terms appearing in the perturbation series are then modeled in the form of an equivalent circuit. This model is subsequently used in the analysis of full-wave rectifier. Matlab simulation results are included which confirm the validity of the theoretical formulations. Perturbation analysis acts a helpful tool in analyzing time-varying systems and chaotic systems.

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

Solitary waves of the Kadomstev-Petviashvili equation in warm dusty plasma with variable dust charge, two temperature ion and nonthermal electron

International Nuclear Information System (INIS)

Pakzad, Hamid Reza

2009-01-01

The propagation of nonlinear waves in warm dusty plasmas with variable dust charge, two temperature ion and nonthermal electron is studied. By using the reductive perturbation theory, the Kadomstev-Petviashivili (KP) equation is derived. Existence of rarefactive and compressive solitons is analyzed.

Analytical Investigation of Beam Deformation Equation using Perturbation, Homotopy Perturbation, Variational Iteration and Optimal Homotopy Asymptotic Methods

DEFF Research Database (Denmark)

Farrokhzad, F.; Mowlaee, P.; Barari, Amin

2011-01-01

The beam deformation equation has very wide applications in structural engineering. As a differential equation, it has its own problem concerning existence, uniqueness and methods of solutions. Often, original forms of governing differential equations used in engineering problems are simplified...... Method (OHAM). The comparisons of the results reveal that these methods are very effective, convenient and quite accurate to systems of non-linear differential equation......., and this process produces noise in the obtained answers. This paper deals with solution of second order of differential equation governing beam deformation using four analytical approximate methods, namely the Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM) and Optimal Homotopy Asymptotic...

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

Science.gov (United States)

Jun, Li; Huicheng, Yin

2018-05-01

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

A discrete homotopy perturbation method for non-linear Schrodinger equation

Directory of Open Access Journals (Sweden)

H. A. Wahab

2015-12-01

Full Text Available A general analysis is made by homotopy perturbation method while taking the advantages of the initial guess, appearance of the embedding parameter, different choices of the linear operator to the approximated solution to the non-linear Schrodinger equation. We are not dependent upon the Adomian polynomials and find the linear forms of the components without these calculations. The discretised forms of the nonlinear Schrodinger equation allow us whether to apply any numerical technique on the discritisation forms or proceed for perturbation solution of the problem. The discretised forms obtained by constructed homotopy provide the linear parts of the components of the solution series and hence a new discretised form is obtained. The general discretised form for the NLSE allows us to choose any initial guess and the solution in the closed form.

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

Dispersion equations for field-aligned cyclotron waves in axisymmetric magnetospheric plasmas

Directory of Open Access Journals (Sweden)

N. I. Grishanov

2006-03-01

Full Text Available In this paper, we derive the dispersion equations for field-aligned cyclotron waves in two-dimensional (2-D magnetospheric plasmas with anisotropic temperature. Two magnetic field configurations are considered with dipole and circular magnetic field lines. The main contribution of the trapped particles to the transverse dielectric permittivity is estimated by solving the linearized Vlasov equation for their perturbed distribution functions, accounting for the cyclotron and bounce resonances, neglecting the drift effects, and assuming the weak connection of the left-hand and right-hand polarized waves. Both the bi-Maxwellian and bi-Lorentzian distribution functions are considered to model the ring current ions and electrons in the dipole magnetosphere. A numerical code has been developed to analyze the dispersion characteristics of electromagnetic ion-cyclotron waves in an electron-proton magnetospheric plasma with circular magnetic field lines, assuming that the steady-state distribution function of the energetic protons is bi-Maxwellian. As in the uniform magnetic field case, the growth rate of the proton-cyclotron instability (PCI in the 2-D magnetospheric plasmas is defined by the contribution of the energetic ions/protons to the imaginary part of the transverse permittivity elements. We demonstrate that the PCI growth rate in the 2-D axisymmetric plasmasphere can be significantly smaller than that for the straight magnetic field case with the same macroscopic bulk parameters.

Traveltime sensitivity kernels for wave equation tomography using the unwrapped phase

KAUST Repository

Djebbi, Ramzi

2014-02-18

Wave equation tomography attempts to improve on traveltime tomography, by better adhering to the requirements of our finite-frequency data. Conventional wave equation tomography, based on the first-order Born approximation followed by cross-correlation traveltime lag measurement, or on the Rytov approximation for the phase, yields the popular hollow banana sensitivity kernel indicating that the measured traveltime at a point is insensitive to perturbations along the ray theoretical path at certain finite frequencies. Using the instantaneous traveltime, which is able to unwrap the phase of the signal, instead of the cross-correlation lag, we derive new finite-frequency traveltime sensitivity kernels. The kernel reflects more the model-data dependency, we typically encounter in full waveform inversion. This result confirms that the hollow banana shape is borne of the cross-correlation lag measurement, which exposes the Born approximations weakness in representing transmitted waves. The instantaneous traveltime can thus mitigate the additional component of nonlinearity introduced by the hollow banana sensitivity kernels in finite-frequency traveltime tomography. The instantaneous traveltime simply represents the unwrapped phase of Rytov approximation, and thus is a good alternative to Born and Rytov to compute the misfit function for wave equation tomography. We show the limitations of the cross-correlation associated with Born approximation for traveltime lag measurement when the source signatures of the measured and modelled data are different. The instantaneous traveltime is proven to be less sensitive to the distortions in the data signature. The unwrapped phase full banana shape of the sensitivity kernels shows smoother update compared to the banana–doughnut kernels. The measurement of the traveltime delay caused by a small spherical anomaly, embedded into a 3-D homogeneous model, supports the full banana sensitivity assertion for the unwrapped phase.

Traveltime sensitivity kernels for wave equation tomography using the unwrapped phase

KAUST Repository

Djebbi, Ramzi; Alkhalifah, Tariq Ali

2014-01-01

Wave equation tomography attempts to improve on traveltime tomography, by better adhering to the requirements of our finite-frequency data. Conventional wave equation tomography, based on the first-order Born approximation followed by cross-correlation traveltime lag measurement, or on the Rytov approximation for the phase, yields the popular hollow banana sensitivity kernel indicating that the measured traveltime at a point is insensitive to perturbations along the ray theoretical path at certain finite frequencies. Using the instantaneous traveltime, which is able to unwrap the phase of the signal, instead of the cross-correlation lag, we derive new finite-frequency traveltime sensitivity kernels. The kernel reflects more the model-data dependency, we typically encounter in full waveform inversion. This result confirms that the hollow banana shape is borne of the cross-correlation lag measurement, which exposes the Born approximations weakness in representing transmitted waves. The instantaneous traveltime can thus mitigate the additional component of nonlinearity introduced by the hollow banana sensitivity kernels in finite-frequency traveltime tomography. The instantaneous traveltime simply represents the unwrapped phase of Rytov approximation, and thus is a good alternative to Born and Rytov to compute the misfit function for wave equation tomography. We show the limitations of the cross-correlation associated with Born approximation for traveltime lag measurement when the source signatures of the measured and modelled data are different. The instantaneous traveltime is proven to be less sensitive to the distortions in the data signature. The unwrapped phase full banana shape of the sensitivity kernels shows smoother update compared to the banana–doughnut kernels. The measurement of the traveltime delay caused by a small spherical anomaly, embedded into a 3-D homogeneous model, supports the full banana sensitivity assertion for the unwrapped phase.

Perturbation theory of a symmetric center within Liénard equations

Science.gov (United States)

Françoise, Jean-Pierre; Xiao, Dongmei

2015-09-01

In this article, we introduce the use of Lambert function to develop further the global perturbation theory of an integrable Liénard equation which displays a symmetric center. We prove a global Morse lemma for the first integral and deduce the existence of an associated Picard-Fuchs system. We revisit previous contributions to first-order perturbation theory with the help of these new analytic techniques and in particular, we check that the fundamental integrals are linearly independent. The Lambert function allows to find an expansion formula for these integrals. We also study the possibility to develop a higher-order perturbation theory. The algorithm of the successive derivatives works in general in the class of analytic functions on the domain D where the level sets of the first integral are ovals. We end the article with some results on the first integral of a symmetric Liénard equation deduced from the algorithm of successive derivatives.

Kerr-CFT and gravitational perturbations

International Nuclear Information System (INIS)

Dias, Oscar J.C.; Reall, Harvey S.; Santos, Jorge E.

2009-01-01

Motivated by the Kerr-CFT conjecture, we investigate perturbations of the near-horizon extreme Kerr spacetime. The Teukolsky equation for a massless field of arbitrary spin is solved. Solutions fall into two classes: normal modes and traveling waves. Imposing suitable (outgoing) boundary conditions, we find that there are no unstable modes. The explicit form of metric perturbations is obtained using the Hertz potential formalism, and compared with the Kerr-CFT boundary conditions. The energy and angular momentum associated with scalar field and gravitational normal modes are calculated. The energy is positive in all cases. The behaviour of second order perturbations is discussed.

Darboux transformation for the NLS equation

International Nuclear Information System (INIS)

Aktosun, Tuncay; Mee, Cornelis van der

2010-01-01

We analyze a certain class of integral equations associated with Marchenko equations and Gel'fand-Levitan equations. Such integral equations arise through a Fourier transformation on various ordinary differential equations involving a spectral parameter. When the integral operator is perturbed by a finite-rank perturbation, we explicitly evaluate the change in the solution in terms of the unperturbed quantities and the finite-rank perturbation. We show that this result provides a fundamental approach to derive Darboux transformations for various systems of ordinary differential operators. We illustrate our theory by providing the explicit Darboux transformation for the Zakharov-Shabat system and show how the potential and wave function change when a simple discrete eigenvalue is added to the spectrum, and thus we also provide a one-parameter family of Darboux transformations for the nonlinear Schroedinger equation.

A Parameter Robust Method for Singularly Perturbed Delay Differential Equations

Directory of Open Access Journals (Sweden)

Erdogan Fevzi

2010-01-01

Full Text Available Uniform finite difference methods are constructed via nonstandard finite difference methods for the numerical solution of singularly perturbed quasilinear initial value problem for delay differential equations. A numerical method is constructed for this problem which involves the appropriate Bakhvalov meshes on each time subinterval. The method is shown to be uniformly convergent with respect to the perturbation parameter. A numerical example is solved using the presented method, and the computed result is compared with exact solution of the problem.

Perturbation Solutions of the Quintic Duffing Equation with Strong Nonlinearities

Directory of Open Access Journals (Sweden)

Mehmet Pakdemirli

Full Text Available The quintic Duffing equation with strong nonlinearities is considered. Perturbation solutions are constructed using two different techniques: The classical multiple scales method (MS and the newly developed multiple scales Lindstedt Poincare method (MSLP. The validity criteria for admissible solutions are derived. Both approximate solutions are contrasted with the numerical solutions. It is found that MSLP provides compatible solution with the numerical solution for strong nonlinearities whereas MS solution fail to produce physically acceptable solution for large perturbation parameters.

Dissipative Nonlinear Schrödinger Equation for Envelope Solitary Rossby Waves with Dissipation Effect in Stratified Fluids and Its Solution

Directory of Open Access Journals (Sweden)

Yunlong Shi

2014-01-01

Full Text Available We solve the so-called dissipative nonlinear Schrödinger equation by means of multiple scales analysis and perturbation method to describe envelope solitary Rossby waves with dissipation effect in stratified fluids. By analyzing the evolution of amplitude of envelope solitary Rossby waves, it is found that the shear of basic flow, Brunt-Vaisala frequency, and β effect are important factors to form the envelope solitary Rossby waves. By employing trial function method, the asymptotic solution of dissipative nonlinear Schrödinger equation is derived. Based on the solution, the effect of dissipation on the evolution of envelope solitary Rossby wave is also discussed. The results show that the dissipation causes a slow decrease of amplitude of envelope solitary Rossby waves and a slow increase of width, while it has no effect on the propagation velocity. That is quite different from the KdV-type solitary waves. It is notable that dissipation has certain influence on the carrier frequency.

(2+1)-dimensional dissipation nonlinear Schrödinger equation for envelope Rossby solitary waves and chirp effect

International Nuclear Information System (INIS)

Li Jin-Yuan; Fang Nian-Qiao; Yuan Xiao-Bo; Zhang Ji; Xue Yu-Long; Wang Xue-Mu

2016-01-01

In the past few decades, the (1+1)-dimensional nonlinear Schrödinger (NLS) equation had been derived for envelope Rossby solitary waves in a line by employing the perturbation expansion method. But, with the development of theory, we note that the (1+1)-dimensional model cannot reflect the evolution of envelope Rossby solitary waves in a plane. In this paper, by constructing a new (2+1)-dimensional multiscale transform, we derive the (2+1)-dimensional dissipation nonlinear Schrödinger equation (DNLS) to describe envelope Rossby solitary waves under the influence of dissipation which propagate in a plane. Especially, the previous researches about envelope Rossby solitary waves were established in the zonal area and could not be applied directly to the spherical earth, while we adopt the plane polar coordinate and overcome the problem. By theoretical analyses, the conservation laws of (2+1)-dimensional envelope Rossby solitary waves as well as their variation under the influence of dissipation are studied. Finally, the one-soliton and two-soliton solutions of the (2+1)-dimensional NLS equation are obtained with the Hirota method. Based on these solutions, by virtue of the chirp concept from fiber soliton communication, the chirp effect of envelope Rossby solitary waves is discussed, and the related impact factors of the chirp effect are given. (paper)

Stabilization of spiral wave and turbulence in the excitable media using parameter perturbation scheme

International Nuclear Information System (INIS)

Ma Jun; Wang Chunni; Li Yanlong; Pu Zhongsheng; Jin Wuyin

2008-01-01

This paper proposes a scheme of parameter perturbation to suppress the stable rotating spiral wave, meandering spiral wave and turbulence in the excitable media, which is described by the modified Fitzhugh–Nagumo (MFHN) model. The controllable parameter in the MFHN model is perturbed with a weak pulse and the pulse period is decided by the rotating period of the spiral wave approximatively. It is confirmed that the spiral wave and spiral turbulence can be suppressed greatly. Drift and instability of spiral wave can be observed in the numerical simulation tests before the whole media become homogeneous finally. (general)

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.

Dynamic behavior of ion acoustic waves in electron-positron-ion magnetoplasmas with superthermal electrons and positrons

Science.gov (United States)

Saha, Asit; Pal, Nikhil; Chatterjee, Prasanta

2014-10-01

The dynamic behavior of ion acoustic waves in electron-positron-ion magnetoplasmas with superthermal electrons and positrons has been investigated in the framework of perturbed and non-perturbed Kadomtsev-Petviashili (KP) equations. Applying the reductive perturbation technique, we have derived the KP equation in electron-positron-ion magnetoplasma with kappa distributed electrons and positrons. Bifurcations of ion acoustic traveling waves of the KP equation are presented. Using the bifurcation theory of planar dynamical systems, the existence of the solitary wave solutions and the periodic traveling wave solutions has been established. Two exact solutions of these waves have been derived depending on the system parameters. Then, using the Hirota's direct method, we have obtained two-soliton and three-soliton solutions of the KP equation. The effect of the spectral index κ on propagations of the two-soliton and the three-soliton has been shown. Considering an external periodic perturbation, we have presented the quasi periodic behavior of ion acoustic waves in electron-positron-ion magnetoplasmas.

Dynamic behavior of ion acoustic waves in electron-positron-ion magnetoplasmas with superthermal electrons and positrons

Energy Technology Data Exchange (ETDEWEB)

Saha, Asit, E-mail: asit-saha123@rediffmail.com, E-mail: prasantachatterjee1@rediffmail.com [Department of Mathematics, Sikkim Manipal Institute of Technology, Majitar, Rangpo, East-Sikkim 737136 (India); Department of Mathematics, Siksha Bhavana, Visva Bharati University, Santiniketan-731235 (India); Pal, Nikhil; Chatterjee, Prasanta, E-mail: asit-saha123@rediffmail.com, E-mail: prasantachatterjee1@rediffmail.com [Department of Mathematics, Siksha Bhavana, Visva Bharati University, Santiniketan-731235 (India)

2014-10-15

The dynamic behavior of ion acoustic waves in electron-positron-ion magnetoplasmas with superthermal electrons and positrons has been investigated in the framework of perturbed and non-perturbed Kadomtsev-Petviashili (KP) equations. Applying the reductive perturbation technique, we have derived the KP equation in electron-positron-ion magnetoplasma with kappa distributed electrons and positrons. Bifurcations of ion acoustic traveling waves of the KP equation are presented. Using the bifurcation theory of planar dynamical systems, the existence of the solitary wave solutions and the periodic traveling wave solutions has been established. Two exact solutions of these waves have been derived depending on the system parameters. Then, using the Hirota's direct method, we have obtained two-soliton and three-soliton solutions of the KP equation. The effect of the spectral index κ on propagations of the two-soliton and the three-soliton has been shown. Considering an external periodic perturbation, we have presented the quasi periodic behavior of ion acoustic waves in electron-positron-ion magnetoplasmas.

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.

Evolution of perturbation in charge-varying dusty plasmas

International Nuclear Information System (INIS)

Popel, S.I.; Golub, A.P.; Losseva, T.V.; Bingham, R.; Benkadda, S.

2001-01-01

The nonstationary problem of the evolution of perturbation and its transformation into nonlinear wave structure in dusty plasmas is considered. For this purpose two one-dimensional models based on a set of fluid equations, Poisson's equation, and a charging equation for dust are developed. The first (simplified) model corresponds to the case [Popel et al., Phys. Plasmas 3, 4313 (1996)] when exact steady-state shock wave solutions can exist. This simplified model includes variable-charged dust grains, Boltzmann electrons, and inertial ions. The second (ionization source) model takes into account the variation of the ion density and the ion momentum dissipation due to dust particle charging as well as the source of plasma particles due to ionization process. The computational method for solving the set of equations which describe the evolution in time of a nonlinear structure in a charge-varying dusty plasma is developed. The case of the evolution of an intensive initial nonmoving region with a constant enhanced ion density is investigated on the basis of these two models. The consideration within the ionization source model is performed for the data of the laboratory experiment [Luo et al., Phys. Plasmas 6, 3455 (1999)]. It is shown that the ionization source model allows one to obtain shock structures as a result of evolution of an initial perturbation and to explain the experimental value of the width of the shock wave front. Comparison of the numerical data obtained on the basis of the ionization source model and the simplified model shows that the main characteristic features of the shock structure are the same for both models. Nevertheless, the ionization source model is much more sensitive to the form of the initial perturbation than the simplified model. The solution of the problem of the evolution of perturbation and its transformation into shock wave in charge-varying dusty plasmas opens up possibilities for description of the real phenomena like supernova

Mean field effects for counterpropagating traveling wave solutions of reaction-diffusion systems

International Nuclear Information System (INIS)

Bernoff, A.J.; Kuske, R.; Matkowsky, B.J.; Volpert, V.

1995-01-01

In many problems, one observes traveling waves that propagate with constant velocity and shape in the χ direction, say, are independent of y, and z and describe transitions between two equilibrium states. As parameters of the system are varied, these traveling waves can become unstable and give rise to waves having additional structure, such as traveling waves in the y and z directions, which can themselves be subject to instabilities as parameters are further varied. To investigate this scenario the authors consider a system of reaction-diffusion equations with a traveling wave solution as a basic state. They determine solutions bifurcating from the basic state that describe counterpropagating traveling wave in directions orthogonal to the direction of propagation of the basic state and determine their stability. Specifically, they derive long wave modulation equations for the amplitudes of the counterpropagating traveling waves that are coupled to an equation for a mean field, generated by the translation of the basic state in the direction of its propagation. The modulation equations are then employed to determine stability boundaries to long wave perturbations for both unidirectional and counterpropagating traveling waves. The stability analysis is delicate because the results depend on the order in which transverse and longitudinal perturbation wavenumbers are taken to zero. For the unidirectional wave they demonstrate that it is sufficient to consider the cases of (1) purely transverse perturbations, (2) purely longitudinal perturbations, and (3) longitudinal perturbations with a small transverse component. These yield Eckhaus type, zigzag type, and skew type instabilities, respectively

A perturbative solution to metadynamics ordinary differential equation

Science.gov (United States)

Tiwary, Pratyush; Dama, James F.; Parrinello, Michele

2015-12-01

Metadynamics is a popular enhanced sampling scheme wherein by periodic application of a repulsive bias, one can surmount high free energy barriers and explore complex landscapes. Recently, metadynamics was shown to be mathematically well founded, in the sense that the biasing procedure is guaranteed to converge to the true free energy surface in the long time limit irrespective of the precise choice of biasing parameters. A differential equation governing the post-transient convergence behavior of metadynamics was also derived. In this short communication, we revisit this differential equation, expressing it in a convenient and elegant Riccati-like form. A perturbative solution scheme is then developed for solving this differential equation, which is valid for any generic biasing kernel. The solution clearly demonstrates the robustness of metadynamics to choice of biasing parameters and gives further confidence in the widely used method.

A perturbative solution to metadynamics ordinary differential equation.

Science.gov (United States)

Tiwary, Pratyush; Dama, James F; Parrinello, Michele

2015-12-21

Metadynamics is a popular enhanced sampling scheme wherein by periodic application of a repulsive bias, one can surmount high free energy barriers and explore complex landscapes. Recently, metadynamics was shown to be mathematically well founded, in the sense that the biasing procedure is guaranteed to converge to the true free energy surface in the long time limit irrespective of the precise choice of biasing parameters. A differential equation governing the post-transient convergence behavior of metadynamics was also derived. In this short communication, we revisit this differential equation, expressing it in a convenient and elegant Riccati-like form. A perturbative solution scheme is then developed for solving this differential equation, which is valid for any generic biasing kernel. The solution clearly demonstrates the robustness of metadynamics to choice of biasing parameters and gives further confidence in the widely used method.

Analysis of the Effect of Electron Density Perturbations Generated by Gravity Waves on HF Communication Links

Science.gov (United States)

Fagre, M.; Elias, A. G.; Chum, J.; Cabrera, M. A.

2017-12-01

In the present work, ray tracing of high frequency (HF) signals in ionospheric disturbed conditions is analyzed, particularly in the presence of electron density perturbations generated by gravity waves (GWs). The three-dimensional numerical ray tracing code by Jones and Stephenson, based on Hamilton's equations, which is commonly used to study radio propagation through the ionosphere, is used. An electron density perturbation model is implemented to this code based upon the consideration of atmospheric GWs generated at a height of 150 km in the thermosphere and propagating up into the ionosphere. The motion of the neutral gas at these altitudes induces disturbances in the background plasma which affects HF signals propagation. To obtain a realistic model of GWs in order to analyze the propagation and dispersion characteristics, a GW ray tracing method with kinematic viscosity and thermal diffusivity was applied. The IRI-2012, HWM14 and NRLMSISE-00 models were incorporated to assess electron density, wind velocities, neutral temperature and total mass density needed for the ray tracing codes. Preliminary results of gravity wave effects on ground range and reflection height are presented for low-mid latitude ionosphere.

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.

Solution of a partial differential equation subject to temperature overspecification by He's homotopy perturbation method

International Nuclear Information System (INIS)

Dehghan, Mehdi; Shakeri, Fatemeh

2007-01-01

In this work, the solution of an inverse problem concerning a diffusion equation with source control parameters is presented. The homotopy perturbation method is employed to solve this equation. This method changes a difficult problem into a simple problem which can be easily solved. In this procedure, according to the homotopy technique, a homotopy with an embedding parameter p element of [0,1] is constructed, and this parameter is considered a 'small parameter', so the method is called the homotopy perturbation method, which can take full advantage of the traditional perturbation method and homotopy technique. The approximations obtained by the proposed method are uniformly valid not only for small parameters, but also for very large parameters. The fact that this technique, in contrast to the traditional perturbation methods, does not require a small parameter in the system, leads to wide applications in nonlinear equations

Numerical analysis of quasiperiodic perturbations for the Alfven wave

International Nuclear Information System (INIS)

Yamakoshi, Y.; Muto, K.; Yoshida, Z.

1994-01-01

The Alfven wave may have a localized eigenfunction when it propagates on a chaotic magnetic field. The Arnold-Beltrami-Childress (ABC) flow is a paradigm of chaotic stream lines and is a simple exact solution to the three-dimensional force-free plasma equilibrium equations. The three-dimensional structure of the magnetic field is represented by sinusoidal quasiperiodic modulation. The short wavelength Alfven wave equation for the ABC-flow magnetic field has a quasiperiodic potential term, which induces interference among ''Bragg-reflected'' waves with irregular phases. Then the eigenfunction decays at long distance and a point spectrum occurs. Two different types of short wavelength modes have numerically analyzed to demonstrate the existence of localized Alfven wave eigenmodes

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.)

Nonlinear electromagnetic waves in a degenerate electron-positron plasma

Energy Technology Data Exchange (ETDEWEB)

El-Labany, S.K., E-mail: skellabany@hotmail.com [Department of Physics, Faculty of Science, Damietta University, New Damietta (Egypt); El-Taibany, W.F., E-mail: eltaibany@hotmail.com [Department of Physics, College of Science for Girls in Abha, King Khalid University, Abha (Saudi Arabia); El-Samahy, A.E.; Hafez, A.M.; Atteya, A., E-mail: ahmedsamahy@yahoo.com, E-mail: am.hafez@sci.alex.edu.eg, E-mail: ahmed_ateya2002@yahoo.com [Department of Physics, Faculty of Science, Alexandria University, Alexandria (Egypt)

2015-08-15

Using the reductive perturbation technique (RPT), the nonlinear propagation of magnetosonic solitary waves in an ultracold, degenerate (extremely dense) electron-positron (EP) plasma (containing ultracold, degenerate electron, and positron fluids) is investigated. The set of basic equations is reduced to a Korteweg-de Vries (KdV) equation for the lowest-order perturbed magnetic field and to a KdV type equation for the higher-order perturbed magnetic field. The solutions of these evolution equations are obtained. For better accuracy and searching on new features, the new solutions are analyzed numerically based on compact objects (white dwarf) parameters. It is found that including the higher-order corrections results as a reduction (increment) of the fast (slow) electromagnetic wave amplitude but the wave width is increased in both cases. The ranges where the RPT can describe adequately the total magnetic field including different conditions are discussed. (author)

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)

A perturbed Lennard-Jones chain equation of state for liquid metals

Energy Technology Data Exchange (ETDEWEB)

Mousazadeh, M H; Marageh, M Ghanadi [AEOI, JIH Research Laboratory, 11365/8486, Tehran (Iran, Islamic Republic of)

2006-05-24

The perturbed Lennard-Jones chain (PLJC) equation of state is formulated based on first-order variational perturbation theory. The model uses two parameters for a monatomic system, segment size, {sigma}, and segment energy, {epsilon}/k. In this work, we employed the PLJC equation to calculate the liquid density of 26 metals, including alkali and alkali earth metals, iron, cobalt, nickel, copper, silver, gold, zinc, cadmium, mercury, aluminium, gallium, indium, thallium, tin, lead, antimony, and bismuth, for which accurate experimental data exist in the literature. The calculations cover a broad range of temperatures ranging from the melting point to close to the critical point and pressures ranging from the vapour-pressure curve up to pressures as high as 2000 bar. The average absolute deviation in the liquid density predicted by the PLJC equation of state in the saturation line compared with experimental data is 1.26%. Also, using the normal melting temperature and liquid density at melting point (T{sub m}, {rho}{sub m}) as input data for the estimation of the equation of state parameters provides a good correlation of liquid density at saturated and compressed pressures.

Perturbation method for periodic solutions of nonlinear jerk equations

International Nuclear Information System (INIS)

Hu, H.

2008-01-01

A Lindstedt-Poincare type perturbation method with bookkeeping parameters is presented for determining accurate analytical approximate periodic solutions of some third-order (jerk) differential equations with cubic nonlinearities. In the process of the solution, higher-order approximate angular frequencies are obtained by Newton's method. A typical example is given to illustrate the effectiveness and simplicity of the proposed method

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

Improved Fluid Perturbation Theory: Equation of state for Fluid Xenon

OpenAIRE

Li, Qiong; Liu, Hai-Feng; Zhang, Gong-Mu; Zhao, Yan-Hong; Tian, Ming-Feng; Song, Hai-Feng

2016-01-01

The traditional fluid perturbation theory is improved by taking electronic excitations and ionizations into account, in the framework of average ion spheres. It is applied to calculate the equation of state for fluid Xenon, which turns out in good agreement with the available shock data.

Decoherence, discord, and the quantum master equation for cosmological perturbations

Science.gov (United States)

Hollowood, Timothy J.; McDonald, Jamie I.

2017-05-01

We examine environmental decoherence of cosmological perturbations in order to study the quantum-to-classical transition and the impact of noise on entanglement during inflation. Given an explicit interaction between the system and environment, we derive a quantum master equation for the reduced density matrix of perturbations, drawing parallels with quantum Brownian motion, where we see the emergence of fluctuation and dissipation terms. Although the master equation is not in Lindblad form, we see how typical solutions exhibit positivity on super-horizon scales, leading to a physically meaningful density matrix. This allows us to write down a Langevin equation with stochastic noise for the classical trajectories which emerge from the quantum system on super-horizon scales. In particular, we find that environmental decoherence increases in strength as modes exit the horizon, with the growth driven essentially by white noise coming from local contributions to environmental correlations. Finally, we use our master equation to quantify the strength of quantum correlations as captured by discord. We show that environmental interactions have a tendency to decrease the size of the discord and that these effects are determined by the relative strength of the expansion rate and interaction rate of the environment. We interpret this in terms of the competing effects of particle creation versus environmental fluctuations, which tend to increase and decrease the discord respectively.

Dynamics of perturbed wavetrain solutions to the Ginzburg-Landau equation

International Nuclear Information System (INIS)

Keefe, L.R.

1984-01-01

The bifurcation structure of even, spatially periodic solutions to the time-dependent Ginzburg-Landau equation is investigated analytically and numerically. A rich variety of behavior, including limit cycles, two-tori, period-doubling sequences, and strange attractors are found to exist in the phase space of the solutions constructed from spatial Fourier modes. Beginning with unstable perturbations to the spatially homogeneous Stokes solution, changes in solution behavior are examined as the perturbing wavenumber q is varied in the range 0.6 to 1.3. Solution bifurcations as q changes are often found to be associated with symmetry making or breaking changes in the structure of attractors in phase space. Two distinct mirror image attractors are found to coexist for many values of q. Chaotic motion is found for two ranges of q Lyapunov exponents of the solutions and the Lyapunov dimension of the corresponding attractors are calculated for the larger of these regions. Poincare sections of the attractors within this chaotic range are consistent with the dimension calculation and also reveal a bifurcation structure within the chaos which broadly resembles that found in one-dimensional quadratic maps. The integrability of the Ginzburg-Landau equation is also examined. It is demonstrated that the equation does not possess the Painleve property, except for a special case of the coefficients which corresponds to the integrable non-linear Schroedinger (NLS) equation

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

Non-perturbative models of intermittency in drift-wave turbulence: towards a probabilistic theory of anomalous transport

International Nuclear Information System (INIS)

Kim, Eun-jin; Diamond, P.H.; Malkov, M.

2003-01-01

Two examples of non-perturbative models of intermittency in drift-wave (DW) turbulence are presented. The first is a calculation of the probability distribution function (PDF) of ion heat flux due to structures in ion temperature gradient turbulence. The instanton calculus predicts the PDF to be a stretched exponential. The second is a derivation of a bi-variate Burgers equation for the evolution of the DW population density in the presence of radially extended streamer flows. The PDF of fluctuation intensity avalanches is determined. The relation of this to turbulence spreading, observed in simulations, is discussed. (author)

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

Analysis and Application of High Resolution Numerical Perturbation Algorithm for Convective-Diffusion Equation

International Nuclear Information System (INIS)

Gao Zhi; Shen Yi-Qing

2012-01-01

The high resolution numerical perturbation (NP) algorithm is analyzed and tested using various convective-diffusion equations. The NP algorithm is constructed by splitting the second order central difference schemes of both convective and diffusion terms of the convective-diffusion equation into upstream and downstream parts, then the perturbation reconstruction functions of the convective coefficient are determined using the power-series of grid interval and eliminating the truncated errors of the modified differential equation. The important nature, i.e. the upwind dominance nature, which is the basis to ensuring that the NP schemes are stable and essentially oscillation free, is firstly presented and verified. Various numerical cases show that the NP schemes are efficient, robust, and more accurate than the original second order central scheme

Finite Amplitude Electron Plasma Waves in a Cylindrical Waveguide

DEFF Research Database (Denmark)

Juul Rasmussen, Jens

1978-01-01

The nonlinear behaviour of the electron plasma wave propagating in a cylindrical plasma waveguide immersed in an infinite axial magnetic field is investigated using the Krylov-Bogoliubov-Mitropolsky perturbation method, by means of which is deduced the nonlinear Schrodinger equation governing...... the long-time slow modulation of the wave amplitude. From this equation the amplitude-dependent frequency and wavenumber shifts are calculated, and it is found that the electron waves with short wavelengths are modulationally unstable with respect to long-wavelength, low-frequency perturbations...

Waves in magnetized quark matter

Science.gov (United States)

Fogaça, D. A.; Sanches, S. M.; Navarra, F. S.

2018-05-01

We study wave propagation in a non-relativistic cold quark-gluon plasma immersed in a constant magnetic field. Starting from the Euler equation we derive linear wave equations and investigate their stability and causality. We use a generic form for the equation of state, the EOS derived from the MIT bag model and also a variant of the this model which includes gluon degrees of freedom. The results of this analysis may be relevant for perturbations propagating through the quark matter phase in the core of compact stars and also for perturbations propagating in the low temperature quark-gluon plasma formed in low energy heavy ion collisions, to be carried out at FAIR and NICA.

A simple electron plasma wave

International Nuclear Information System (INIS)

Brodin, G.; Stenflo, L.

2017-01-01

Considering a class of solutions where the density perturbations are functions of time, but not of space, we derive a new exact large amplitude wave solution for a cold uniform electron plasma. This result illustrates that most simple analytical solutions can appear even if the density perturbations are large. - Highlights: • The influence of large amplitude electromagnetic waves on electrostatic oscillations is found. • A generalized Mathieu equation is derived. • Anharmonic wave profiles are computed numerically.

A simple electron plasma wave

Energy Technology Data Exchange (ETDEWEB)

Brodin, G., E-mail: gert.brodin@physics.umu.se [Department of Physics, Umeå University, SE-901 87 Umeå (Sweden); Stenflo, L. [Department of Physics, Linköping University, SE-581 83 Linköping (Sweden)

2017-03-18

Considering a class of solutions where the density perturbations are functions of time, but not of space, we derive a new exact large amplitude wave solution for a cold uniform electron plasma. This result illustrates that most simple analytical solutions can appear even if the density perturbations are large. - Highlights: • The influence of large amplitude electromagnetic waves on electrostatic oscillations is found. • A generalized Mathieu equation is derived. • Anharmonic wave profiles are computed numerically.

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

International Nuclear Information System (INIS)

Zhang Huiqun

2009-01-01

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

Analysis of a renormalization group method and normal form theory for perturbed ordinary differential equations

Science.gov (United States)

DeVille, R. E. Lee; Harkin, Anthony; Holzer, Matt; Josić, Krešimir; Kaper, Tasso J.

2008-06-01

For singular perturbation problems, the renormalization group (RG) method of Chen, Goldenfeld, and Oono [Phys. Rev. E. 49 (1994) 4502-4511] has been shown to be an effective general approach for deriving reduced or amplitude equations that govern the long time dynamics of the system. It has been applied to a variety of problems traditionally analyzed using disparate methods, including the method of multiple scales, boundary layer theory, the WKBJ method, the Poincaré-Lindstedt method, the method of averaging, and others. In this article, we show how the RG method may be used to generate normal forms for large classes of ordinary differential equations. First, we apply the RG method to systems with autonomous perturbations, and we show that the reduced or amplitude equations generated by the RG method are equivalent to the classical Poincaré-Birkhoff normal forms for these systems up to and including terms of O(ɛ2), where ɛ is the perturbation parameter. This analysis establishes our approach and generalizes to higher order. Second, we apply the RG method to systems with nonautonomous perturbations, and we show that the reduced or amplitude equations so generated constitute time-asymptotic normal forms, which are based on KBM averages. Moreover, for both classes of problems, we show that the main coordinate changes are equivalent, up to translations between the spaces in which they are defined. In this manner, our results show that the RG method offers a new approach for deriving normal forms for nonautonomous systems, and it offers advantages since one can typically more readily identify resonant terms from naive perturbation expansions than from the nonautonomous vector fields themselves. Finally, we establish how well the solution to the RG equations approximates the solution of the original equations on time scales of O(1/ɛ).

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).

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.)

STABILITY THEOREM FOR A CLASS OF PERTURBED NONAUTONOMOUS NEUTRAL DIFFERENTIAL EQUATION WITH UNBOUNDED DELAY

Institute of Scientific and Technical Information of China (English)

无

2008-01-01

In this paper, we consider a one-dimensional nonautonomous neutral differential equation. We obtain sufficient conditions under which the zero solution to this equation with unbounded delay and perturbation is uniformly asymptotically stable.

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....

On Perturbative Cubic Nonlinear Schrodinger Equations under Complex Nonhomogeneities and Complex Initial Conditions

Directory of Open Access Journals (Sweden)

Magdy A. El-Tawil

2009-01-01

Full Text Available A perturbing nonlinear Schrodinger equation is studied under general complex nonhomogeneities and complex initial conditions for zero boundary conditions. The perturbation method together with the eigenfunction expansion and variational parameters methods are used to introduce an approximate solution for the perturbative nonlinear case for which a power series solution is proved to exist. Using Mathematica, the symbolic solution algorithm is tested through computing the possible approximations under truncation procedures. The method of solution is illustrated through case studies and figures.

Coupling between a Langmuir wave and a ballistic perturbation

International Nuclear Information System (INIS)

Gervais, F.; Olivain, J.; Quemeneur, A.; Trocheris, M.

1980-01-01

The study of the mode-mode coupling usually neglects the ballistic contribution associated with parent waves. If this approximation is not made, a new mode, resulting from the interaction between the ballistic perturbation of pulsation ω 2 associated with one launched wave and the Landau component of pulsation ω 1 of the second one appears if ω 1 >ω 2 . The problem is solved theoretically and experimental evidence of this mode from measurements performed on a D.C. plasma column, confirms the results of this analysis

Second-Order Perturbation Theory for Generalized Active Space Self-Consistent-Field Wave Functions.

Science.gov (United States)

Ma, Dongxia; Li Manni, Giovanni; Olsen, Jeppe; Gagliardi, Laura

2016-07-12

A multireference second-order perturbation theory approach based on the generalized active space self-consistent-field (GASSCF) wave function is presented. Compared with the complete active space (CAS) and restricted active space (RAS) wave functions, GAS wave functions are more flexible and can employ larger active spaces and/or different truncations of the configuration interaction expansion. With GASSCF, one can explore chemical systems that are not affordable with either CASSCF or RASSCF. Perturbation theory to second order on top of GAS wave functions (GASPT2) has been implemented to recover the remaining electron correlation. The method has been benchmarked by computing the chromium dimer ground-state potential energy curve. These calculations show that GASPT2 gives results similar to CASPT2 even with a configuration interaction expansion much smaller than the corresponding CAS expansion.

Simulation of Irregular Waves and Wave Induced Loads on Wind Power Plants in Shallow Water

Energy Technology Data Exchange (ETDEWEB)

Trumars, Jenny [Chalmers Univ. of Technology, Goeteborg (Sweden). Dept. of Water Environment Transport

2004-05-01

The essay gives a short introduction to waves and discusses the problem with non-linear waves in shallow water and how they effect an offshore wind energy converter. The focus is on the realisation of non-linear waves in the time domain from short-term statistics in the form of a variance density spectrum of the wave elevation. For this purpose the wave transformation from deep water to the near to shore site of a wind energy farm at Bockstigen has been calculated with the use of SWAN (Simulating Waves Near Shore). The result is a wave spectrum, which can be used as input to the realisation. The realisation of waves is done by perturbation theory to the first and second-order. The properties calculated are the wave elevation, water particle velocity and acceleration. The wave heights from the second order perturbation equations are higher than those from the first order perturbation equations. This is also the case for the water particle kinematics. The increase of variance is significant between the first order and the second order realisation. The calculated wave elevation exhibits non-linear features as the peaks become sharper and the troughs flatter. The resulting forces are calculated using Morison's equation. For second order force and base moment there is an increase in the maximum values. The force and base moment are largest approximately at the zero up and down crossing of the wave elevation. This indicates an inertia dominated wave load. So far the flexibility and the response of the structure have not been taken into account. They are, however, of vital importance. For verification of the wave model the results will later on be compared with measurements at Bockstigen off the coast of Gotland in the Baltic Sea.

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.

Exact Solutions of Atmospheric (2+1)-Dimensional Nonlinear Incompressible Non-hydrostatic Boussinesq Equations

Science.gov (United States)

Liu, Ping; Wang, Ya-Xiong; Ren, Bo; Li, Jin-Hua

2016-12-01

Exact solutions of the atmospheric (2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, several expansion coefficient equations are derived. Symmetries and similarity solutions are researched in order to obtain exact solutions of the INHB equations. Three types of symmetry reduction equations and similarity solutions for the expansion coefficient equations are proposed. Non-traveling wave solutions for the INHB equations are obtained by symmetries of the expansion coefficient equations. Making traveling wave transformations on expansion coefficient equations, we demonstrate some traveling wave solutions of the INHB equations. The evolutions on the wind velocities, temperature perturbation and pressure perturbation are demonstrated by figures, which demonstrate the periodic evolutions with time and space. Supported by the National Natural Science Foundation of China under Grant Nos. 11305031 and 11305106, and Training Programme Foundation for Outstanding Young Teachers in Higher Education Institutions of Guangdong Province under Grant No. Yq2013205

Quasitravelling waves

International Nuclear Information System (INIS)

Beklaryan, Leva A

2011-01-01

A finite difference analogue of the wave equation with potential perturbation is investigated, which simulates the behaviour of an infinite rod under the action of an external longitudinal force field. For a homogeneous rod, describing solutions of travelling wave type is equivalent to describing the full space of classical solutions to an induced one-parameter family of functional differential equations of point type, with the characteristic of the travelling wave as parameter. For an inhomogeneous rod, the space of solutions of travelling wave type is trivial, and their 'proper' extension is defined as solutions of 'quasitravelling' wave type. By contrast to the case of a homogeneous rod, describing the solutions of quasitravelling wave type is equivalent to describing the quotient of the full space of impulsive solutions to an induced one-parameter family of point-type functional differential equations by an equivalence relation connected with the definition of solutions of quasitravelling wave type. Stability of stationary solutions is analyzed. Bibliography: 9 titles.

A perturbation expansion for the nonlinear Schroedinger equation with application to the influence of nonlinear Landau damping

International Nuclear Information System (INIS)

Weiland, J.; Ichikawa, Y.H.; Wilhelmsson, H.

1977-12-01

The Bogoliubov-Mitropolsky perturbation method has been applied to the study of a perturbation on soliton solutions to the nonlinear Schroedinger equation. The results are compared to those of Karpman and Maslov using the inverse scattering method and to those by Ott and Sudan on the KdV equation. (auth.)

The Schroedinger equation as a singular perturbation problem

International Nuclear Information System (INIS)

Jager, E.M. de; Kuepper, T.

1978-01-01

Comparisons are made of the eigenvalues and the corresponding eigenfunctions of the eigenvalue problem connected with the one dimensional Schroedinger equation in Hilbert space. The difference of the eigenvalues is estimated by applying Weyl's monotonicity principle and the minimum maximum principle. The difference of the eigenfunctions is estimated in L 2 norm and in maximum norm obtained by using simple tools from operator theory in Hilbert spaces. An application concerning perturbations of the Planck ideal linear oscillator is given. (author)

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

Effect of a relative phase of waves constituting the initial perturbation and the wave interference on the dynamics of strong-shock-driven Richtmyer-Meshkov flows

Science.gov (United States)

Pandian, Arun; Stellingwerf, Robert F.; Abarzhi, Snezhana I.

2017-07-01

While it is a common wisdom that initial conditions influence the evolution of the Richtmyer-Meshkov instability (RMI), the research in this area is focused primarily on the effects of the wavelength and amplitude of the interface perturbation. The information has hitherto largely ignored the influences on RMI dynamics of the relative phase of waves constituting a multiwave initial perturbation and the interference of the perturbation waves. In this work we systematically study the influence of the relative phase and the interference of waves constituting a multiwave initial perturbation on a strong-shock-driven Richtmyer-Meshkov unstable interface separating ideal fluids with contrast densities. We apply group theory analysis and smoothed particle hydrodynamics numerical simulations. For verification and validation of the simulations, qualitative and quantitative comparisons are performed with rigorous zeroth-order, linear, and nonlinear theories as well as with gas dynamics experiments achieving good agreement. For a sample case of a two-wave (two-mode) initial perturbation we select the first-wave amplitude enabling the maximum initial growth rate of the RMI and we vary the second-wave amplitude from 1% to 100% of the first-wave amplitude. We also vary the relative phase of the first and second waves and consider the in-phase, the antiphase and the random-phase cases. We find that the relative phase and the interference of waves are important factors of RMI dynamics influencing qualitatively and quantitatively the symmetry, morphology, and growth rate of the Richtmyer-Meshkov unstable interface, as well as the order and disorder in strong-shock-driven RMI.

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.

Exact perturbation theory of multiphoton processes at high intensities. [Schroedinger equation, perturbation theory, matrix

Energy Technology Data Exchange (ETDEWEB)

Faisal, F H.M. [Bielefeld Univ. (Germany, F.R.). Fakultaet fuer Physik

1976-06-11

In this work the perturbation theory for multiphoton processes at high intensities is investigated and it is described an analytical method of summing the perturbation series to extract the contribution from all terms that give rise to the absorption of N photons by an atomic system. The method is first applied to the solution of a simple model problem and the result is confirmed by direct integration of the model Schroedinger equation. The usual lowest (nonvanishing)-order perturbation-theoretical calculation is also carried out for this model to demonstrate explicitly that the full result correctly reproduces that of the lowest-order theory in the limit of low intensity. The method is then extended to the case of an atomic system with well-developed spectrum (e.g. H atom) and the N-photon T-matrix is derived in terms of a ''photon matrix'' asub(N), for which a three-term recurrence relation is established. Next, from the vantage point of the general result obtained here, A probe is made into the nature of several approximate nonperturbative solutions that have appeared in the literature in the past. It is shown here that their applicability is severely restricted by the requirement of the essential spectral degeneracy of the atomic system. Finally, appendix A outlines a prescription of computing the photon matrix asub(N), which (as in the usual lowest-order perturbation-theoretical calculation)requires a knowledge of the eigenfunctions and eigenvalues of the atomic Hamiltonian only.

New optical solitons of space-time conformable fractional perturbed Gerdjikov-Ivanov equation by sine-Gordon equation method

Science.gov (United States)

Yaşar, Elif; Yıldırım, Yakup; Yaşar, Emrullah

2018-06-01

This paper devotes to conformable fractional space-time perturbed Gerdjikov-Ivanov (GI) equation which appears in nonlinear fiber optics and photonic crystal fibers (PCF). We consider the model with full nonlinearity in order to give a generalized flavor. The sine-Gordon equation approach is carried out to model equation for retrieving the dark, bright, dark-bright, singular and combined singular optical solitons. The constraint conditions are also reported for guaranteeing the existence of these solitons. We also present some graphical simulations of the solutions for better understanding the physical phenomena of the behind the considered model.

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.

Approximate solution fuzzy pantograph equation by using homotopy perturbation method

Science.gov (United States)

Jameel, A. F.; Saaban, A.; Ahadkulov, H.; Alipiah, F. M.

2017-09-01

In this paper, Homotopy Perturbation Method (HPM) is modified and formulated to find the approximate solution for its employment to solve (FDDEs) involving a fuzzy pantograph equation. The solution that can be obtained by using HPM is in the form of infinite series that converge to the actual solution of the FDDE and this is one of the benefits of this method In addition, it can be used for solving high order fuzzy delay differential equations directly without reduction to a first order system. Moreover, the accuracy of HPM can be detected without needing the exact solution. The HPM is studied for fuzzy initial value problems involving pantograph equation. Using the properties of fuzzy set theory, we reformulate the standard approximate method of HPM and obtain the approximate solutions. The effectiveness of the proposed method is demonstrated for third order fuzzy pantograph equation.

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.

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.

Perturbative expansion and the initial value problem of the K.d.V. equations

International Nuclear Information System (INIS)

Turchetti, G.

1980-01-01

For the potential K.d.V. equation is considered a perturbation expansion in which the initial condition is imposed on the zeroth order term. The N soliton solutions turn out to be rational functions in the expansion parameter so that the perturbation series can be exactly summed by the [N-1/N] Pade approximants; moreover the [n-1/n] and [n/n] Pade approximants for n [pt

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).

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

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].

Perturbation Solutions for Random Linear Structural Systems subject to Random Excitation using Stochastic Differential Equations

DEFF Research Database (Denmark)

Köyluoglu, H.U.; Nielsen, Søren R.K.; Cakmak, A.S.

1994-01-01

perturbation method using stochastic differential equations. The joint statistical moments entering the perturbation solution are determined by considering an augmented dynamic system with state variables made up of the displacement and velocity vector and their first and second derivatives with respect......The paper deals with the first and second order statistical moments of the response of linear systems with random parameters subject to random excitation modelled as white-noise multiplied by an envelope function with random parameters. The method of analysis is basically a second order...... to the random parameters of the problem. Equations for partial derivatives are obtained from the partial differentiation of the equations of motion. The zero time-lag joint statistical moment equations for the augmented state vector are derived from the Itô differential formula. General formulation is given...

Topological horseshoes in travelling waves of discretized nonlinear wave equations

International Nuclear Information System (INIS)

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

2014-01-01

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

Topological horseshoes in travelling waves of discretized nonlinear wave equations

Energy Technology Data Exchange (ETDEWEB)

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

2014-04-15

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

Exponentially Stable Stationary Solutions for Stochastic Evolution Equations and Their Perturbation

International Nuclear Information System (INIS)

Caraballo, Tomas; Kloeden, Peter E.; Schmalfuss, Bjoern

2004-01-01

We consider the exponential stability of stochastic evolution equations with Lipschitz continuous non-linearities when zero is not a solution for these equations. We prove the existence of anon-trivial stationary solution which is exponentially stable, where the stationary solution is generated by the composition of a random variable and the Wiener shift. We also construct stationary solutions with the stronger property of attracting bounded sets uniformly. The existence of these stationary solutions follows from the theory of random dynamical systems and their attractors. In addition, we prove some perturbation results and formulate conditions for the existence of stationary solutions for semilinear stochastic partial differential equations with Lipschitz continuous non-linearities

Stability of Equilibrium Points of Fractional Difference Equations with Stochastic Perturbations

Directory of Open Access Journals (Sweden)

Shaikhet Leonid

2008-01-01

Full Text Available It is supposed that the fractional difference equation , has an equilibrium point and is exposed to additive stochastic perturbations type of that are directly proportional to the deviation of the system state from the equilibrium point . It is shown that known results in the theory of stability of stochastic difference equations that were obtained via V. Kolmanovskii and L. Shaikhet general method of Lyapunov functionals construction can be successfully used for getting of sufficient conditions for stability in probability of equilibrium points of the considered stochastic fractional difference equation. Numerous graphical illustrations of stability regions and trajectories of solutions are plotted.

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.

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

Directory of Open Access Journals (Sweden)

Mostafa M.A. Khater

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

Nonlinear metric perturbation enhancement of primordial gravitational waves.

Science.gov (United States)

Bastero-Gil, M; Macias-Pérez, J; Santos, D

2010-08-20

We present the evolution of the full set of Einstein equations during preheating after inflation. We study a generic supersymmetric model of hybrid inflation, integrating fields and metric fluctuations in a 3-dimensional lattice. We take initial conditions consistent with Einstein's constraint equations. The induced preheating of the metric fluctuations is not large enough to backreact onto the fields, but preheating of the scalar modes does affect the evolution of vector and tensor modes. In particular, they do enhance the induced stochastic background of gravitational waves during preheating, giving an energy density in general an order of magnitude larger than that obtained by evolving the tensor fluctuations in an homogeneous background metric. This enhancement can improve the expectations for detection by planned gravitational wave observatories.

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.

Perturbed invariant subspaces and approximate generalized functional variable separation solution for nonlinear diffusion-convection equations with weak source

Science.gov (United States)

Xia, Ya-Rong; Zhang, Shun-Li; Xin, Xiang-Peng

2018-03-01

In this paper, we propose the concept of the perturbed invariant subspaces (PISs), and study the approximate generalized functional variable separation solution for the nonlinear diffusion-convection equation with weak source by the approximate generalized conditional symmetries (AGCSs) related to the PISs. Complete classification of the perturbed equations which admit the approximate generalized functional separable solutions (AGFSSs) is obtained. As a consequence, some AGFSSs to the resulting equations are explicitly constructed by way of examples.

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.

Cosmological perturbation effects on gravitational-wave luminosity distance estimates

Science.gov (United States)

Bertacca, Daniele; Raccanelli, Alvise; Bartolo, Nicola; Matarrese, Sabino

2018-06-01

Waveforms of gravitational waves provide information about a variety of parameters for the binary system merging. However, standard calculations have been performed assuming a FLRW universe with no perturbations. In reality this assumption should be dropped: we show that the inclusion of cosmological perturbations translates into corrections to the estimate of astrophysical parameters derived for the merging binary systems. We compute corrections to the estimate of the luminosity distance due to velocity, volume, lensing and gravitational potential effects. Our results show that the amplitude of the corrections will be negligible for current instruments, mildly important for experiments like the planned DECIGO, and very important for future ones such as the Big Bang Observer.

Local density approximation for a perturbative equation of state

International Nuclear Information System (INIS)

Astrakharchik, G. E.

2005-01-01

Knowledge of a series expansion of the equation of state provides a deep insight into the physical nature of a quantum system. Starting from a generic 'perturbative' equation of state of a homogeneous ultracold gas we make predictions for the properties of the gas in the presence of harmonic confinement. The local density approximation is used to obtain the chemical potential, total and release energies, Thomas-Fermi size, and density profile of a trapped system in three-, two-, and one-dimensional geometries. The frequencies of the lowest breathing modes are calculated using scaling and sum-rule approaches and could be used in an experiment as a high-precision tool for obtaining the expansion terms of the equation of state. The derived formalism is applied to dilute Bose and Fermi gases in different dimensions and to integrable one-dimensional models. The physical meaning of the expansion terms in a number of systems is discussed

The effect of lower-hybrid waves on the propagation of hydromagnetic waves

International Nuclear Information System (INIS)

Hamabata, Hiromitsu; Namikawa, Tomikazu; Mori, Kazuhiro

1988-01-01

Propagation characteristics of hydromagnetic waves in a magnetic plasma are investigated using the two-plasma fluid equations including the effect of lower-hybrid waves propagating perpendicularly to the magnetic field. The effect of lower-hybrid waves on the propagation of hydromagnetic waves is analysed in terms of phase speed, growth rate, refractive index, polarization and the amplitude relation between the density perturbation and the magnetic-field perturbation for the cases when hydromagnetic waves propagate in the plane whose normal is perpendicular to both the magnetic field and the propagation direction of lower-hybrid waves and in the plane perpendicular to the propagation direction of lower-hybrid waves. It is shown that hydromagnetic waves propagating at small angles to the propagation direction of lower-hybrid waves can be excited by the effect of lower-hybrid waves and the energy of excited waves propagates nearly parallel to the propagation direction of lower-hybrid waves. (author)

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.

Nonlinear wave propagation through a ferromagnet with damping in ...

Indian Academy of Sciences (India)

magnetic waves in a ferromagnet can be reduced to an integro-differential equation. Keywords. Solitons; integro-differential equations; reductive perturbation method. PACS Nos 41.20 Jb; 05.45 Yv; 03.50 De; 78.20 Ls. 1. Introduction. The phenomenon of propagation of electromagnetic waves in ferromagnets are not only.

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)

Non-perturbative analytical solutions of the space- and time-fractional Burgers equations

International Nuclear Information System (INIS)

Momani, Shaher

2006-01-01

Non-perturbative analytical solutions for the generalized Burgers equation with time- and space-fractional derivatives of order α and β, 0 < α, β ≤ 1, are derived using Adomian decomposition method. The fractional derivatives are considered in the Caputo sense. The solutions are given in the form of series with easily computable terms. Numerical solutions are calculated for the fractional Burgers equation to show the nature of solution as the fractional derivative parameter is changed

Linear force and moment equations for an annular smooth shaft seal perturbed both angularly and laterally

Science.gov (United States)

Fenwick, J.; Dijulio, R.; Ek, M. C.; Ehrgott, R.

1982-01-01

Coefficients are derived for equations expressing the lateral force and pitching moments associated with both planar translation and angular perturbations from a nominally centered rotating shaft with respect to a stationary seal. The coefficients for the lowest order and first derivative terms emerge as being significant and are of approximately the same order of magnitude as the fundamental coefficients derived by means of Black's equations. Second derivative, shear perturbation, and entrance coefficient variation effects are adjudged to be small.

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

Projector Augmented-Wave formulation of response to strain and electric field perturbation within the density-functional perturbation theory

Science.gov (United States)

Martin, Alexandre; Torrent, Marc; Caracas, Razvan

2015-03-01

A formulation of the response of a system to strain and electric field perturbations in the pseudopotential-based density functional perturbation theory (DFPT) has been proposed by D.R Hamman and co-workers. It uses an elegant formalism based on the expression of DFT total energy in reduced coordinates, the key quantity being the metric tensor and its first and second derivatives. We propose to extend this formulation to the Projector Augmented-Wave approach (PAW). In this context, we express the full elastic tensor including the clamped-atom tensor, the atomic-relaxation contributions (internal stresses) and the response to electric field change (piezoelectric tensor and effective charges). With this we are able to compute the elastic tensor for all materials (metals and insulators) within a fully analytical formulation. The comparison with finite differences calculations on simple systems shows an excellent agreement. This formalism has been implemented in the plane-wave based DFT ABINIT code. We apply it to the computation of elastic properties and seismic-wave velocities of iron with impurity elements. By analogy with the materials contained in meteorites, tested impurities are light elements (H, O, C, S, Si).

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

Modélisation de l'imagerie biomédicale hybride par perturbations mécaniques

OpenAIRE

Seppecher , Laurent

2014-01-01

This thesis aims at developing an original mathematical approach for modeling hybrid biomedical imaging modalities. The core idea is to run an ill-posed imaging method while perturbing the medium using mechanical displacements. These displacements described by an elastic wave equation perturb the collected measurements. Using these perturbed measurements and taking advantage of the perturbation localizing e↵ect, it is possible to significantly overcome the resolution of the basic method. The ...

A collective variable approach and stabilization for dispersion-managed optical solitons in the quintic complex Ginzburg-Landau equation as perturbations of the nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Fewo, S I; Kenfack-Jiotsa, A; Kofane, T C

2006-01-01

With the help of the one-dimensional quintic complex Ginzburg-Landau equation (CGLE) as perturbations of the nonlinear Schroedinger equation (NLSE), we derive the equations of motion of pulse parameters called collective variables (CVs), of a pulse propagating in dispersion-managed (DM) fibre optic links. The equations obtained are investigated numerically in order to view the evolution of pulse parameters along the propagation distance, and also to analyse effects of initial amplitude and width on the propagating pulse. Nonlinear gain is shown to be beneficial in stabilizing DM solitons. A fully numerical simulation of the one-dimensional quintic CGLE as perturbations of NLSE finally tests the results of the CV theory. A good agreement is observed between both methods

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.

Nonlinear modulation of ionization waves

International Nuclear Information System (INIS)

Bekki, Naoaki

1981-01-01

In order to investigate the nonlinear characteristics of ionization waves (moving-striations) in the positive column of glow discharge, a nonlinear modulation of ionization waves in the region of the Pupp critical current is analysed by means of the reductive perturbation method. The modulation of ionization waves is described by a nonlinear Schroedinger type equation. The coefficients of the equation are evaluated using the data of the low pressure Argon-discharge, and the simple solutions (plane wave and envelope soliton type solutions) are presented. Under a certain condition an envelope soliton is propagated through the positive column. (author)

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.

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....

Perturbative renormalization of composite operators via flow equations. Pt. 2

International Nuclear Information System (INIS)

Keller, G.; Kopper, C.

1993-01-01

We give a rigorous and very detailed derivation of the short distance expansion for a product of two arbitrary composite operators in the framework of the perturbative Euclidean massive Φ 4 4 . The technically almost trivial proof rests on an extension of the differential flow equation method to Green functions with bilocal insertions, for which we also establish a set of generalized Zimmermann identities and Lowenstein rules. (orig.)

Propagation of perturbations for a sixth-order thin film equation

Directory of Open Access Journals (Sweden)

Zhenbang Li

2012-07-01

Full Text Available We consider an initial-boundary problem for a sixth-order thin film equation, which arises in the industrial application of the isolation oxidation of silicon. Relying on some necessary uniform estimates of the approximate solutions, we prove the existence of radial symmetric solutions to this problem in the two-dimensional space. The nonnegativity and the finite speed of propagation of perturbations of solutions are also discussed.

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.)

Ambipolarons: Solitary wave solutions for the radial electric field in a plasma

International Nuclear Information System (INIS)

Hastings, D.E.; Hazeltine, R.D.; Morrison, P.J.

1986-01-01

The ambipolar radial electric field in a nonaxisymmetric plasma can be described by a nonlinear diffusion equation. This equation is shown to possess solitary wave solutions. A model nonlinear diffusion equation with a cubic nonlinearity is studied. An explicit analytic step-like form for the solitary wave is found. It is shown that the solitary wave solutions are linearly stable against all but translational perturbations. Collisions of these solitary waves are studied and three possible final states are found: two diverging solitary waves, two stationary solitary waves, or two converging solitary waves leading to annihilation

Some applications of perturbation theory to numerical integration methods for the Schroedinger equation

International Nuclear Information System (INIS)

Killingbeck, J.

1979-01-01

By using the methods of perturbation theory it is possible to construct simple formulae for the numerical integration of the Schroedinger equation, and also to calculate expectation values solely by means of simple eigenvalue calculations. (Auth.)

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.

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.

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.

Boundary mediated position control of traveling waves

Science.gov (United States)

Martens, Steffen; Ziepke, Alexander; Engel, Harald

Reaction control is an essential task in biological systems and chemical process industry. Often, the excitable medium supporting wave propagation exhibits an irregular shape and/or is limited in size. In particular, the analytic treatment of wave phenomena is notoriously difficult due to the spatial modulation of the domain's. Recently, we have provided a first systematic treatment by applying asymptotic perturbation analysis leading to an approximate description that involves a reduction of dimensionality; the 3D RD equation with spatially dependent NFBCs on the reactants reduces to a 1D reaction-diffusion-advection equation. Here, we present a novel method to control the position ϕ (t) of traveling waves in modulated domains according to a prespecified protocol of motion. Given this protocol, the ``optimal'' geometry of reactive domains Q (x) is found as the solution of the perturbatively derived equation of motion. Noteworthy, such a boundary control can be expressed in terms of the uncontrolled wave profile and its propagation velocity, rendering detailed knowledge of the reaction kinetics unnecessary. German Science Foundation DFG through the SFB 910 ''Control of Self-Organizing Nonlinear Systems''.

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...

Dynamical criteria for rogue waves in nonlinear Schrödinger models

International Nuclear Information System (INIS)

Calini, Annalisa; Schober, Constance M

2012-01-01

We investigate rogue waves in deep water in the framework of the nonlinear Schrödinger (NLS) and Dysthe equations. Amongst the homoclinic orbits of unstable NLS Stokes waves, we seek good candidates to model actual rogue waves. In this paper we propose two selection criteria: stability under perturbations of initial data, and persistence under perturbations of the NLS model. We find that requiring stability selects homoclinic orbits of maximal dimension. Persistence under (a particular) perturbation selects a homoclinic orbit of maximal dimension all of whose spatial modes are coalesced. These results suggest that more realistic sea states, described by JONSWAP power spectra, may be analyzed in terms of proximity to NLS homoclinic data. In fact, using the NLS spectral theory, we find that rogue wave events in random oceanic sea states are well predicted by proximity to homoclinic data of the NLS equation. (invited article)

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 ...

Analysis of perturbation methods for rearrangement collisions: Comparison of distorted-wave and coupled-channel-wave transition amplitudes

International Nuclear Information System (INIS)

Suck Salk, S.H.

1985-01-01

With the use of projection operators, the formal expressions of distorted-wave and coupled-channel-wave transition amplitudes for rearrangement collisions are derived. Use of projection operators (for the transition amplitudes) sharpens our understanding of the structural differences between the two transition amplitudes. The merit of each representation of the transition amplitudes is discussed. Derived perturbation potentials are found to have different structures. The rigorously derived distorted-wave Born-approximation (DWBA) transition amplitude is shown to be a generalization of the earlier DWBA expression obtained from the assumption of the dominance of elastic scattering in rearrangement collisions

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.

Gauge-invariant perturbations in a spatially flat anisotropic universe

International Nuclear Information System (INIS)

Den, Mitsue.

1986-12-01

The gauge-invariant perturbations in a spatially flat anisotropic universe with an arbitrary dimension (= N) are studied. In a previous paper the equations for the perturbations with a wave vector k a in one of the axial directions were derived and their solutions were shown. In this paper the perturbations with k a in arbitrary directions are treated. The remarkable properties are that all three types (scalar, vector, and tensor) of perturbations are generally coupled, so that a density perturbation can be produced also by vector or tensor perturbations. The formulation is quite general, but the behavior of the perturbations is discussed in a simple case such that N = 4 and k a is orthogonal to one of the axial directions. In this case, the perturbations are divided into two groups which are dynamically decoupled from each other. The asymptotic behavior of the perturbations in the group containing the density perturbation is discussed. (author)

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

Soliton solutions of the two-dimensional KdV-Burgers equation by homotopy perturbation method

International Nuclear Information System (INIS)

Molabahrami, A.; Khani, F.; Hamedi-Nezhad, S.

2007-01-01

In this Letter, the He's homotopy perturbation method (HPM) to finding the soliton solutions of the two-dimensional Korteweg-de Vries Burgers' equation (tdKdVB) for the initial conditions was applied. Numerical solutions of the equation were obtained. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. The results reveal that the HPM is very effective and simple

Non-Linear Langmuir Wave Modulation in Collisionless Plasmas

DEFF Research Database (Denmark)

Dysthe, K. B.; Pécseli, Hans

1977-01-01

in the expressions concerning the modulation instability of a plane Langmuir wave. When the Vlasov equation for the ions is applied, a Langmuir wave is modulationally unstable for arbitrary perturbations independent of the unperturbed wave amplitude, in contrast to what is found for fluid ions. A simple analogy...

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

Wave propagation in spatially modulated tubes

Energy Technology Data Exchange (ETDEWEB)

Ziepke, A., E-mail: ziepke@itp.tu-berlin.de; Martens, S.; Engel, H. [Institut für Theoretische Physik, Hardenbergstraße 36, EW 7-1, Technische Universität Berlin, 10623 Berlin (Germany)

2016-09-07

We investigate wave propagation in rotationally symmetric tubes with a periodic spatial modulation of cross section. Using an asymptotic perturbation analysis, the governing quasi-two-dimensional reaction-diffusion equation can be reduced into a one-dimensional reaction-diffusion-advection equation. Assuming a weak perturbation by the advection term and using projection method, in a second step, an equation of motion for traveling waves within such tubes can be derived. Both methods predict properly the nonlinear dependence of the propagation velocity on the ratio of the modulation period of the geometry to the intrinsic width of the front, or pulse. As a main feature, we observe finite intervals of propagation failure of waves induced by the tube’s modulation and derive an analytically tractable condition for their occurrence. For the highly diffusive limit, using the Fick-Jacobs approach, we show that wave velocities within modulated tubes are governed by an effective diffusion coefficient. Furthermore, we discuss the effects of a single bottleneck on the period of pulse trains. We observe period changes by integer fractions dependent on the bottleneck width and the period of the entering pulse train.

Nonlinear sausage-wave propagation in a magnetic slab in an incompressible fluid

International Nuclear Information System (INIS)

Ruderman, M.S.

1993-01-01

Long nonlinear sausage-wave propagation in a magnetic slab in an incompressible plasma is considered. The governing equation is derived with the aid of the reductive perturbation method. The solutions of this equation in the form of periodic waves of permanent shape are found numerically. (Author)

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

Modulated amplitude waves in Bose-Einstein condensates

International Nuclear Information System (INIS)

Porter, Mason A.; Cvitanovic, Predrag

2004-01-01

We analyze spatiotemporal structures in the Gross-Pitaevskii equation to study the dynamics of quasi-one-dimensional Bose-Einstein condensates (BECs) with mean-field interactions. A coherent structure ansatz yields a parametrically forced nonlinear oscillator, to which we apply Lindstedt's method and multiple-scale perturbation theory to determine the dependence of the intensity of periodic orbits ('modulated amplitude waves') on their wave number. We explore BEC band structure in detail using Hamiltonian perturbation theory and supporting numerical simulations

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.

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.

Quantal Brownian Motion from RPA dynamics: The master and Fokker-Planck equations

International Nuclear Information System (INIS)

Yannouleas, C.

1984-05-01

From the purely quantal RPA description of the damped harmonic oscillator and of the corresponding Brownian Motion within the full space (phonon subspace plus reservoir), a master equation (as well as a Fokker-Planck equation) for the reduced density matrix (for the reduced Wigner function, respectively) within the phonon subspace is extracted. The RPA master equation agrees with the master equation derived by the time-dependent perturbative approaches which utilize Tamm-Dancoff Hilbert spaces and invoke the rotating wave approximation. Since the RPA yields a full, as well as a contracted description, it can account for both the kinetic and the unperturbed oscillator momenta. The RPA description of the quantal Brownian Motion contrasts with the descriptions provided by the time perturbative approaches whether they invoke or not the rotating wave approximation. The RPA description also contrasts with the phenomenological phase space quantization. (orig.)

An acoustic eikonal equation for attenuating transversely isotropic media with a vertical symmetry axis

KAUST Repository

Hao, Qi

2016-11-21

Seismic-wave attenuation is an important component of describing wave propagation. Certain regions, such as gas clouds inside the earth, exert highly localized attenuation. In fact, the anisotropic nature of the earth induces anisotropic attenuation because the quasi P-wave dispersion effect should be profound along the symmetry direction. We have developed a 2D acoustic eikonal equation governing the complex-valued traveltime of quasi P-waves in attenuating, transversely isotropic media with a vertical-symmetry axis (VTI). This equation is derived under the assumption that the complex-valued traveltime of quasi P-waves in attenuating VTI media are independent of the S-wave velocity parameter υS0 in Thomsen\\'s notation and the S-wave attenuation coefficient AS0 in Zhu and Tsvankin\\'s notation. We combine perturbation theory and Shanks transform to develop practical approximations to the acoustic attenuating eikonal equation, capable of admitting an analytical description of the attenuation in homogeneous media. For a horizontal-attenuating VTI layer, we also derive the nonhyperbolic approximations for the real and imaginary parts of the complex-valued reflection traveltime. These equations reveal that (1) the quasi SV-wave velocity and the corresponding quasi SV-wave attenuation coefficient given as part of Thomsen-type notation barely affect the ray velocity and ray attenuation of quasi P-waves in attenuating VTI media; (2) combining the perturbation method and Shanks transform provides an accurate analytic eikonal solution for homogeneous attenuating VTI media; (3) for a horizontal attenuating VTI layer with weak attenuation, the real part of the complex-valued reflection traveltime may still be described by the existing nonhyperbolic approximations developed for nonattenuating VTI media, and the imaginary part of the complex-valued reflection traveltime still has the shape of nonhyperbolic curves. In addition, we have evaluated the possible extension of the

Study on thermal wave based on the thermal mass theory

Institute of Scientific and Technical Information of China (English)

无

2009-01-01

The conservation equations for heat conduction are established based on the concept of thermal mass.We obtain a general heat conduction law which takes into account the spatial and temporal inertia of thermal mass.The general law introduces a damped thermal wave equation.It reduces to the well-known CV model when the spatial inertia of heat flux and temperature and the temporal inertia of temperature are neglected,which indicates that the CV model only considers the temporal inertia of heat flux.Numerical simulations on the propagation and superposition of thermal waves show that for small thermal perturbation the CV model agrees with the thermal wave equation based on the thermal mass theory.For larger thermal perturbation,however,the physically impossible phenomenon pre-dicted by CV model,i.e.the negative temperature induced by the thermal wave superposition,is eliminated by the general heat conduction law,which demonstrates that the present heat conduction law based on the thermal mass theory is more reasonable.

Study on thermal wave based on the thermal mass theory

Institute of Scientific and Technical Information of China (English)

HU RuiFeng; CAO BingYang

2009-01-01

The conservation equations for heat conduction are established based on the concept of thermal mass. We obtain a general heat conduction law which takes into account the spatial and temporal inertia of thermal mass. The general law introduces a damped thermal wave equation. It reduces to the well-known CV model when the spatial inertia of heat flux and temperature and the temporal inertia of temperature are neglected, which indicates that the CV model only considers the temporal inertia of heat flux. Numerical simulations on the propagation and superposition of thermal waves show that for small thermal perturbation the CV model agrees with the thermal wave equation based on the thermal mass theory. For larger thermal perturbation, however, the physically impossible phenomenon pre-dicted by CV model, i.e. the negative temperature induced by the thermal wave superposition, is eliminated by the general heat conduction law, which demonstrates that the present heat conduction law based on the thermal mass theory is more reasonable.

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)

Influence of the interaction of ions-dust grains on ion acoustic wave and dust acoustic wave

International Nuclear Information System (INIS)

Hua Jianjun; Liu Jinyuan; Ma Tengcai

2004-01-01

Based on a set of hydrodynamic equations and a linear time-dependent perturbation theory, the influence of the interaction of ions-dust grains on ion acoustic wave IAW and dust acoustic wave DAW in dusty plasma is analyzed. The results show that the interaction makes IAW more stable and DAW less stable

Degenerate RS perturbation theory. [Rayleigh-Schroedinger energies and wave functions

Science.gov (United States)

Hirschfelder, J. O.; Certain, P. R.

1974-01-01

A concise, systematic procedure is given for determining the Rayleigh-Schroedinger energies and wave functions of degenerate states to arbitrarily high orders even when the degeneracies of the various states are resolved in arbitrary orders. The procedure is expressed in terms of an iterative cycle in which the energy through the (2n + 1)-th order is expressed in terms of the partially determined wave function through the n-th order. Both a direct and an operator derivation are given. The two approaches are equivalent and can be transcribed into each other. The direct approach deals with the wave functions (without the use of formal operators) and has the advantage that it resembles the usual treatment of nondegenerate perturbations and maintains close contact with the basic physics. In the operator approach, the wave functions are expressed in terms of infinite-order operators which are determined by the successive resolution of the space of the zeroth-order functions.

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.

Gravitational waves from the axial perturbations of hyperon stars

International Nuclear Information System (INIS)

Wen De-Hua; Yan Jing; Liu Xue-Mei

2012-01-01

The eigen-frequencies of the axial w-mode oscillations of hyperon stars are examined. It is shown that as the appearance of hyperons softens the equation of state of the super-density matter, the frequency of gravitational waves from the axial w-mode of hyperon star becomes smaller than that of a traditional neutron star at the same stellar mass. Moreover, the eigenfrequencies of hyperon stars also have scaling universality. It is shown that the EURO third-generation gravitational-wave detector has the potential to detect the gravitational-wave signal emitted from the axial w-mode oscillations of a hyperon star. (general)

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...

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.

Explicit formulas for generalized harmonic perturbations of the infinite quantum well with an application to Mathieu equations

International Nuclear Information System (INIS)

García-Ravelo, J.; Trujillo, A. L.; Schulze-Halberg, A.

2012-01-01

We obtain explicit formulas for perturbative corrections of the infinite quantum well model. The formulas we obtain are based on a class of matrix elements that we construct by means of two-parameter ladder operators associated with the infinite quantum well system. Our approach can be used to construct solutions to Schrödinger-type equations that involve generalized harmonic perturbations of their potentials, such as cosine powers, Fourier series, and more general functions. As a particular case, we obtain characteristic values for odd periodic solutions of the Mathieu equation.

Explicit formulas for generalized harmonic perturbations of the infinite quantum well with an application to Mathieu equations

Energy Technology Data Exchange (ETDEWEB)

Garcia-Ravelo, J.; Trujillo, A. L. [Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Unidad Profesional Adolfo Lopez Mateos, Zacatenco, 07738 Mexico D.F. (Mexico); Schulze-Halberg, A. [Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States)

2012-10-15

We obtain explicit formulas for perturbative corrections of the infinite quantum well model. The formulas we obtain are based on a class of matrix elements that we construct by means of two-parameter ladder operators associated with the infinite quantum well system. Our approach can be used to construct solutions to Schroedinger-type equations that involve generalized harmonic perturbations of their potentials, such as cosine powers, Fourier series, and more general functions. As a particular case, we obtain characteristic values for odd periodic solutions of the Mathieu equation.

Application of Homotopy-Perturbation Method to Nonlinear Ozone Decomposition of the Second Order in Aqueous Solutions Equations

DEFF Research Database (Denmark)

Ganji, D.D; Miansari, Mo; B, Ganjavi

2008-01-01

In this paper, homotopy-perturbation method (HPM) is introduced to solve nonlinear equations of ozone decomposition in aqueous solutions. HPM deforms a di¢ cult problem into a simple problem which can be easily solved. The effects of some parameters such as temperature to the solutions are consid......In this paper, homotopy-perturbation method (HPM) is introduced to solve nonlinear equations of ozone decomposition in aqueous solutions. HPM deforms a di¢ cult problem into a simple problem which can be easily solved. The effects of some parameters such as temperature to the solutions...

Multidimensional behavior of an electrostatic ion wave in a magnetized plasma

International Nuclear Information System (INIS)

Nishinari, K.; Abe, K.; Satsuma, J.

1994-01-01

Three-dimensional nonlinear evolution equations of an electrostatic ion wave in the short wave region in a magnetized plasma are derived by means of the reductive perturbation method. It is shown that, in some cases, the evolution equations reduce to the Davey--Stewartson 1 equations, which are known to admit solutions with localized structure in higher dimension. It is also shown that there is a possibility of collapse of localized structure in the case of wave propagation parallel to a magnetic field

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)

Relativistic many-body perturbation-theory calculations based on Dirac-Fock-Breit wave functions

International Nuclear Information System (INIS)

Ishikawa, Y.; Quiney, H.M.

1993-01-01

A relativistic many-body perturbation theory based on the Dirac-Fock-Breit wave functions has been developed and implemented by employing analytic basis sets of Gaussian-type functions. The instantaneous Coulomb and low-frequency Breit interactions are treated using a unified formalism in both the construction of the Dirac-Fock-Breit self-consistent-field atomic potential and in the evaluation of many-body perturbation-theory diagrams. The relativistic many-body perturbation-theory calculations have been performed on the helium atom and ions of the helium isoelectronic sequence up to Z=50. The contribution of the low-frequency Breit interaction to the relativistic correlation energy is examined for the helium isoelectronic sequence

Evolution of rogue waves in dusty plasmas

Energy Technology Data Exchange (ETDEWEB)

Tolba, R. E., E-mail: tolba-math@yahoo.com; El-Bedwehy, N. A., E-mail: nab-elbedwehy@yahoo.com [Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517 (Egypt); Moslem, W. M., E-mail: wmmoslem@hotmail.com [Department of Physics, Faculty of Science, Port Said University, Port Said 42521 (Egypt); Centre for Theoretical Physics, The British University in Egypt (BUE), El-Shorouk City, Cairo (Egypt); El-Labany, S. K., E-mail: skellabany@hotmail.com [Department of Physics, Faculty of Science, Damietta University, New Damietta 34517 (Egypt)

2015-04-15

The evolution of rogue waves associated with the dynamics of positively charged dust grains that interact with streaming electrons and ions is investigated. Using a perturbation method, the basic set of fluid equations is reduced to a nonlinear Schrödinger equation (NLSE). The rational solution of the NLSE is presented, which proposed as an effective tool for studying the rogue waves in Jupiter. It is found that the existence region of rogue waves depends on the dust-acoustic speed and the streaming densities of the ions and electrons. Furthermore, the supersonic rogue waves are much taller than the subsonic rogue waves by ∼25 times.

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...

Mono-implicit Runge Kutta schemes for singularly perturbed delay differential equations

Science.gov (United States)

Rihan, Fathalla A.; Al-Salti, Nasser S.

2017-09-01

In this paper, we adapt Mono-Implicit Runge-Kutta schemes for numerical approximations of singularly perturbed delay differential equations. The schemes are developed to reduce the computational cost of the fully implicit method which combine the accuracy of implicit method and efficient implementation. Numerical stability properties of the schemes are investigated. Numerical simulations are provided to show the effectiveness of the method for both stiff and non-stiff initial value problems.

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

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

Wave equation tomography using the unwrapped phase - Analysis of the traveltime sensitivity kernels

KAUST Repository

Djebbi, Ramzi

2013-01-01

Full waveform inversion suffers from the high non-linearity in the misfit function, which causes the convergence to a local minimum. In the other hand, traveltime tomography has a quasi-linear misfit function but yields low- resolution models. Wave equation tomography (WET) tries to improve on traveltime tomography, by better adhering to the requirements of our finite-frequency data. However, conventional (WET), based on the crosscorelaion lag, yields the popular hallow banana sensitivity kernel indicating that the measured wavefield at a point is insensitive to perturbations along the ray theoretical path at certain finite frequencies. Using the instantaneous traveltime, the sensitivity kernel reflects more the model-data dependency we grown accustom to in seismic inversion (even phase inversion). Demonstrations on synthetic and the Mamousi model support such assertions.

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

Nonlinear waves and weak turbulence

CERN Document Server

Zakharov, V E

1997-01-01

This book is a collection of papers on dynamical and statistical theory of nonlinear wave propagation in dispersive conservative media. Emphasis is on waves on the surface of an ideal fluid and on Rossby waves in the atmosphere. Although the book deals mainly with weakly nonlinear waves, it is more than simply a description of standard perturbation techniques. The goal is to show that the theory of weakly interacting waves is naturally related to such areas of mathematics as Diophantine equations, differential geometry of waves, Poincaré normal forms, and the inverse scattering method.

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...

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)

A statistical study of ionopause perturbation and associated boundary wave formation at Venus.

Science.gov (United States)

Chong, G. S.; Pope, S. A.; Walker, S. N.; Zhang, T.; Balikhin, M. A.

2017-12-01

In contrast to Earth, Venus does not possess an intrinsic magnetic field. Hence the interaction between solar wind and Venus is significantly different when compared to Earth, even though these two planets were once considered similar. Within the induced magnetosphere and ionosphere of Venus, previous studies have shown the existence of ionospheric boundary waves. These structures may play an important role in the atmospheric evolution of Venus. By using Venus Express data, the crossings of the ionopause boundary are determined based on the observations of photoelectrons during 2011. Pulses of dropouts in the electron energy spectrometer were observed in 92 events, which suggests potential perturbations of the boundary. Minimum variance analysis of the 1Hz magnetic field data for the perturbations is conducted and used to confirm the occurrence of the boundary waves. Statistical analysis shows that they were propagating mainly in the ±VSO-Y direction in the polar north terminator region. The generation mechanisms of boundary waves and their evolution into the potential nonlinear regime are discussed and analysed.

Nonlinear modulation of ion acoustic waves in a magnetized plasma

International Nuclear Information System (INIS)

Bharuthram, R.; Shukla, P.K.

1987-01-01

The quasistatic plasma slow response to coherent ion acoustic waves in a magnetized plasma is considered. A multidimensional cubic nonlinear Schroedinger equation is derived. It is found that the ion acoustic waves remain modulationally stable against oblique perturbations

Stability of time-dependent particle-like solutions of some wave equations

International Nuclear Information System (INIS)

Voronov, N.A.

1978-01-01

The proof of the nonstability of the one-dimensional periodical localized solutions of the equation with a spontaneously broken symmetry is given. The stability of the one-dimensional oscillating solutions of the sine-Gordon equation was also considered with regard to such perturbations. As it was expected these solutions proved to be stable

A high-order perturbation of surfaces method for scattering of linear waves by periodic multiply layered gratings in two and three dimensions

Science.gov (United States)

Hong, Youngjoon; Nicholls, David P.

2017-09-01

The capability to rapidly and robustly simulate the scattering of linear waves by periodic, multiply layered media in two and three dimensions is crucial in many engineering applications. In this regard, we present a High-Order Perturbation of Surfaces method for linear wave scattering in a multiply layered periodic medium to find an accurate numerical solution of the governing Helmholtz equations. For this we truncate the bi-infinite computational domain to a finite one with artificial boundaries, above and below the structure, and enforce transparent boundary conditions there via Dirichlet-Neumann Operators. This is followed by a Transformed Field Expansion resulting in a Fourier collocation, Legendre-Galerkin, Taylor series method for solving the problem in a transformed set of coordinates. Assorted numerical simulations display the spectral convergence of the proposed algorithm.

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...

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

Asymptotic behavior of monodromy singularly perturbed differential equations on a Riemann surface

CERN Document Server

Simpson, Carlos

1991-01-01

This book concerns the question of how the solution of a system of ODE's varies when the differential equation varies. The goal is to give nonzero asymptotic expansions for the solution in terms of a parameter expressing how some coefficients go to infinity. A particular classof families of equations is considered, where the answer exhibits a new kind of behavior not seen in most work known until now. The techniques include Laplace transform and the method of stationary phase, and a combinatorial technique for estimating the contributions of terms in an infinite series expansion for the solution. Addressed primarily to researchers inalgebraic geometry, ordinary differential equations and complex analysis, the book will also be of interest to applied mathematicians working on asymptotics of singular perturbations and numerical solution of ODE's.

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

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.

Surface perturbations of a shallow viscous fluid heated from below and the (2+1)-dimensional Burgers equation

International Nuclear Information System (INIS)

Kraenkel, R.A.; Pereira, J.G.; Manna, M.A.

1991-01-01

The (2+1)-dimensional Burgers equation is obtained as the equation of motion governing the surface perturbations of a shallow viscous fluid heated from below, provided the Rayleigh number of the system satisfy the condition R ≠ 30. A solution to this equation is explicity exhibited and it is argued that it describes the nonlinear evolution of a nearly one-dimensional kink. (author)

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.

Investigation of solutions of boundary-value singular perturbated problem for Schroedinger equation of 4th order

International Nuclear Information System (INIS)

Amirkhanov, I.V.; Zhidkov, E.P.; Konnova, S.V.

2000-01-01

For the case of spherical-symmetrical potential we have considered the convergence of the solution of singular-perturbated Schroedinger equation of the 4th order to the solution of the corresponding standard nonrelativistic Schroedinger equation by numerical and analytical methods. The questions of existence of the solutions are explored. Numerical results are given. (author)

Born approximation to a perturbative numerical method for the solution of the Schroedinger equation

International Nuclear Information System (INIS)

Adam, Gh.

1978-01-01

A step function perturbative numerical method (SF-PN method) is developed for the solution of the Cauchy problem for the second order liniar differential equation in normal form. An important point stressed in the present paper, which seems to have been previously ignored in the literature devoted to the PN methods, is the close connection between the first order perturbation theory of the PN approach and the wellknown Born approximation, and, in general, the connection between the varjous orders of the PN corrections and the Neumann series. (author)

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.

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.

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

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.

A nonlinear inversion for the velocity background and perturbation models

KAUST Repository

Wu, Zedong

2015-08-19

Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI) by inverting for the single scattered wavefield obtained using an image. However, current RWI methods usually neglect diving waves, which is an important source of information for extracting the long wavelength components of the velocity model. Thus, we propose a new optimization problem through breaking the velocity model into the background and the perturbation in the wave equation directly. In this case, the perturbed model is no longer the single scattering model, but includes all scattering. We optimize both components simultaneously, and thus, the objective function is nonlinear with respect to both the background and perturbation. The new introduced w can absorb the non-smooth update of background naturally. Application to the Marmousi model with frequencies that start at 5 Hz shows that this method can converge to the accurate velocity starting from a linearly increasing initial velocity. Application to the SEG2014 demonstrates the versatility of the approach.

A Lie-Deprit perturbation algorithm for linear differential equations with periodic coefficients

OpenAIRE

Casas Pérez, Fernando; Chiralt Monleon, Cristina

2014-01-01

A perturbative procedure based on the Lie-Deprit algorithm of classical mechanics is proposed to compute analytic approximations to the fundamental matrix of linear di erential equations with periodic coe cients. These approximations reproduce the structure assured by the Floquet theorem. Alternatively, the algorithm provides explicit approximations to the Lyapunov transformation reducing the original periodic problem to an autonomous sys- tem and also to its characteristic ...

On the multisummability of WKB solutions of certain singularly perturbed linear ordinary differential equations

Directory of Open Access Journals (Sweden)

Yoshitsugu Takei

2015-01-01

Full Text Available Using two concrete examples, we discuss the multisummability of WKB solutions of singularly perturbed linear ordinary differential equations. Integral representations of solutions and a criterion for the multisummability based on the Cauchy-Heine transform play an important role in the proof.

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

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

Covariant approach of perturbations in Lovelock type brane gravity

Science.gov (United States)

Bagatella-Flores, Norma; Campuzano, Cuauhtemoc; Cruz, Miguel; Rojas, Efraín

2016-12-01

We develop a covariant scheme to describe the dynamics of small perturbations on Lovelock type extended objects propagating in a flat Minkowski spacetime. The higher-dimensional analogue of the Jacobi equation in this theory becomes a wave type equation for a scalar field Φ . Whithin this framework, we analyse the stability of membranes with a de Sitter geometry where we find that the Jacobi equation specializes to a Klein-Gordon (KG) equation for Φ possessing a tachyonic mass. This shows that, to some extent, these types of extended objects share the symmetries of the Dirac-Nambu-Goto (DNG) action which is by no means coincidental because the DNG model is the simplest included in this type of gravity.

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

Shock-wave structure formation in a dusty plasma

International Nuclear Information System (INIS)

Popel', S.I.; Golub', A.P.; Loseva, T.V.; Bingkhem, R.; Benkadda, S.

2001-01-01

Nonstationary problem on evolution perturbation and its transformation into nonlinear wave structure is considered. The method developed permits finding solution to the system of nonlinear evolution equations describing dust particles with variable charge, Boltzmann electron and inertia ions. An accurate stationary solution as ion-sonic wave structures explained by anomalous dissipation due to electric discharge of dust particles was found. Evolution of two types of initial perturbations was studied, i.e.: soliton and immobile region with increased density of ions - a step. Soliton evolution in plasma with variable charge of dust particles results in the appearance on nonstationary shock-wave structure, whereas the step evolution gives rise to appearance of a shock wave similar to the stationary one along with rarefaction wave [ru

Mode coupling of Schwarzschild perturbations: Ringdown frequencies

International Nuclear Information System (INIS)

Pazos, Enrique; Brizuela, David; Martin-Garcia, Jose M.; Tiglio, Manuel

2010-01-01

Within linearized perturbation theory, black holes decay to their final stationary state through the well-known spectrum of quasinormal modes. Here we numerically study whether nonlinearities change this picture. For that purpose we study the ringdown frequencies of gauge-invariant second-order gravitational perturbations induced by self-coupling of linearized perturbations of Schwarzschild black holes. We do so through high-accuracy simulations in the time domain of first and second-order Regge-Wheeler-Zerilli type equations, for a variety of initial data sets. We consider first-order even-parity (l=2, m=±2) perturbations and odd-parity (l=2, m=0) ones, and all the multipoles that they generate through self-coupling. For all of them and all the initial data sets considered we find that--in contrast to previous predictions in the literature--the numerical decay frequencies of second-order perturbations are the same ones of linearized theory, and we explain the observed behavior. This would indicate, in particular, that when modeling or searching for ringdown gravitational waves, appropriately including the standard quasinormal modes already takes into account nonlinear effects.

Development of a nonresonant perturbation technique and its application to multicell traveling-wave deflectors

Energy Technology Data Exchange (ETDEWEB)

Tan, Jianhao [Shanghai Institute of Applied Physics, Chinese Academy of Science, Shanghai 201800 (China); Shanghai Science Research Center, Chinese Academy of Science, Shanghai 201204 (China); Tong, Dechun [Department of Engineering Physics, Tsinghua University, Beijing 100084 (China); Gu, Qiang; Fang, Wencheng [Shanghai Institute of Applied Physics, Chinese Academy of Science, Shanghai 201800 (China); Shanghai Science Research Center, Chinese Academy of Science, Shanghai 201204 (China); Zhao, Zhentang, E-mail: zhaozhentang@sinap.ac.cn [Shanghai Institute of Applied Physics, Chinese Academy of Science, Shanghai 201800 (China); Shanghai Key Laboratory of Cryogenics & Superconducting RF Technology, Shanghai 201800 (China); Shanghai Science Research Center, Chinese Academy of Science, Shanghai 201204 (China)

2016-11-01

A tuning method augmented by the bead-pull technique based on nonresonant perturbation field distribution measurements has been widely applied for traveling-wave (TW) accelerating structures. The method is also suitable for deflecting structures, but some key considerations of the field components of the HEM{sub 11} mode and the selection of bead merit discussion. A “cage”-type perturbing object has been designed, fabricated and applied in nonresonant perturbation measurements. Measurements on an S-band TW deflecting structure are carried out, and the measurement and tuning method will be used on the newly developed X-band deflecting structure at Shanghai Institute of Applied Physics.

Development of a nonresonant perturbation technique and its application to multicell traveling-wave deflectors

International Nuclear Information System (INIS)

Tan, Jianhao; Tong, Dechun; Gu, Qiang; Fang, Wencheng; Zhao, Zhentang

2016-01-01

A tuning method augmented by the bead-pull technique based on nonresonant perturbation field distribution measurements has been widely applied for traveling-wave (TW) accelerating structures. The method is also suitable for deflecting structures, but some key considerations of the field components of the HEM_1_1 mode and the selection of bead merit discussion. A “cage”-type perturbing object has been designed, fabricated and applied in nonresonant perturbation measurements. Measurements on an S-band TW deflecting structure are carried out, and the measurement and tuning method will be used on the newly developed X-band deflecting structure at Shanghai Institute of Applied Physics.

Perturbation theory with respect to intercenter electron exchange and superexchange with degeneracy

International Nuclear Information System (INIS)

Orlenko, E.V.; Rumyantsev, A.A.

1990-01-01

The corrections to the energy and wave functions of a multielectron system of interacting atoms are calculated in a general analytic form by taking into account degeneracy of the states in accordance with the Young schemes. The rule for writing down the perturbation operator in such systems is formulated in the case when the ground and excited state vectors are antisymmetrized with respect to interchange of electrons between the centers. A secular equation of the theory is derived by applying perturbation theory, one of the parameters of which is the degree of overlap of the wave functions. Some concrete examples of interatomic interactions of an unpaired nature which are due to exchange and superexchange effects are considered

Ion Acceleration in Plasmas with Alfven Waves

International Nuclear Information System (INIS)

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

2005-01-01

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

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

A modified Friedmann equation for a system with varying gravitational mass

Science.gov (United States)

Gorkavyi, Nick; Vasilkov, Alexander

2018-05-01

The Laser Interferometer Gravitational-Wave Observatory (LIGO) detection of gravitational waves that take away 5 per cent of the total mass of two merging black holes points out on the importance of considering varying gravitational mass of a system. Using an assumption that the energy-momentum pseudo-tensor of gravitational waves is not considered as a source of gravitational field, we analyse a perturbation of the Friedmann-Robertson-Walker metric caused by the varying gravitational mass of a system. This perturbation leads to a modified Friedmann equation that contains a term similar to the `cosmological constant'. Theoretical estimates of the effective cosmological constant quantitatively corresponds to observed cosmological acceleration.

Gravitational, shear and matter waves in Kantowski-Sachs cosmologies

Energy Technology Data Exchange (ETDEWEB)

Keresztes, Zoltán; Gergely, László Á. [Department of Theoretical Physics, University of Szeged, Tisza Lajos krt 84-86, Szeged 6720 (Hungary); Forsberg, Mats; Bradley, Michael [Department of Physics, UmeåUniversity (Sweden); Dunsby, Peter K.S., E-mail: zkeresztes@titan.physx.u-szeged.hu, E-mail: forsberg.mats.a.b@gmail.com, E-mail: michael.bradley@physics.umu.se, E-mail: peter.dunsby@uct.ac.za, E-mail: gergely@physx.u-szeged.hu [Astrophysics, Cosmology and Gravity Centre (ACGC), University of Cape Town, Rondebosch 7701, Cape Town (South Africa)

2015-11-01

A general treatment of vorticity-free, perfect fluid perturbations of Kantowski-Sachs models with a positive cosmological constant are considered within the framework of the 1+1+2 covariant decomposition of spacetime. The dynamics is encompassed in six evolution equations for six harmonic coefficients, describing gravito-magnetic, kinematic and matter perturbations, while a set of algebraic expressions determine the rest of the variables. The six equations further decouple into a set of four equations sourced by the perfect fluid, representing forced oscillations and two uncoupled damped oscillator equations. The two gravitational degrees of freedom are represented by pairs of gravito-magnetic perturbations. In contrast with the Friedmann case one of them is coupled to the matter density perturbations, becoming decoupled only in the geometrical optics limit. In this approximation, the even and odd tensorial perturbations of the Weyl tensor evolve as gravitational waves on the anisotropic Kantowski-Sachs background, while the modes describing the shear and the matter density gradient are out of phase dephased by π /2 and share the same speed of sound.

On a transformation of Tuekolsky's equation and the electromagnetic perturbation of the Kerr black hole

Energy Technology Data Exchange (ETDEWEB)

Chandrasekhar, S [Chicago Univ., Ill. (USA)

1976-02-10

Teukolsky's equation, governing the perturbations (scalar, electromagnetic, and gravitational) of the Kerr black hole, is transformed, by a simple change of variables, in a manner such that there is formally no difference in the treatments of the axisymmetric and the non-axisymmetric modes: the role of 'm' is effectively eliminated. By considering in detail the case of electromagentic perturbations it is shown how, in all cases, the problems can be reduced to problems in the theory of penetration of one dimensional potential barriers with, however, certain novel features. The phenomenon of super-radiance, peculiar to the Kerr metric, emerges, for example, in an unexpected guise. The case of scalar perturbations is considered briefly in an appendix.

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)

Internal wave energy flux from density perturbations in nonlinear stratifications

Science.gov (United States)

Lee, Frank M.; Allshouse, Michael R.; Swinney, Harry L.; Morrison, P. J.

2017-11-01

Tidal flow over the topography at the bottom of the ocean, whose density varies with depth, generates internal gravity waves that have a significant impact on the energy budget of the ocean. Thus, understanding the energy flux (J = p v) is important, but it is difficult to measure simultaneously the pressure and velocity perturbation fields, p and v . In a previous work, a Green's-function-based method was developed to calculate the instantaneous p, v , and thus J , given a density perturbation field for a constant buoyancy frequency N. Here we extend the previous analytic Green's function work to include nonuniform N profiles, namely the tanh-shaped and linear cases, because background density stratifications that occur in the ocean and some experiments are nonlinear. In addition, we present a finite-difference method for the general case where N has an arbitrary profile. Each method is validated against numerical simulations. The methods we present can be applied to measured density perturbation data by using our MATLAB graphical user interface EnergyFlux. PJM was supported by the U.S. Department of Energy Contract DE-FG05-80ET-53088. HLS and MRA were supported by ONR Grant No. N000141110701.

Solution to the Diffusion equation for multi groups in X Y geometry using Linear Perturbation theory

International Nuclear Information System (INIS)

Mugica R, C.A.

2004-01-01

Diverse methods exist to solve numerically the neutron diffusion equation for several energy groups in stationary state among those that highlight those of finite elements. In this work the numerical solution of this equation is presented using Raviart-Thomas nodal methods type finite element, the RT0 and RT1, in combination with iterative techniques that allow to obtain the approached solution in a quick form. Nevertheless the above mentioned, the precision of a method is intimately bound to the dimension of the approach space by cell, 5 for the case RT0 and 12 for the RT1, and/or to the mesh refinement, that makes the order of the problem of own value to solve to grow considerably. By this way if it wants to know an acceptable approach to the value of the effective multiplication factor of the system when this it has experimented a small perturbation it was appeal to the Linear perturbation theory with which is possible to determine it starting from the neutron flow and of the effective multiplication factor of the not perturbed case. Results are presented for a reference problem in which a perturbation is introduced in an assemble that simulates changes in the control bar. (Author)

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.

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 (G/G)-expansion method and travelling wave ...

Indian Academy of Sciences (India)

In this paper, we construct the travelling wave solutions to the perturbed nonlinear Schrödinger's equation (NLSE) with Kerr law non-linearity by the extended (′/)-expansion method. Based on this method, we obtain abundant exact travelling wave solutions of NLSE with Kerr law nonlinearity with arbitrary parameters.

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

Approximate Solution of Schrödinger Equation with Pseudo-Gaussian Potential Viewed as a Perturbation

Directory of Open Access Journals (Sweden)

Iacob Theodor-Felix

2015-12-01

Full Text Available We consider the Schrödinger equation with pseudo-Gaussian potential and point out that it is basically made up by a term representing the harmonic oscillator potential and an additional term, which is actually a power series that converges rapidly. Based on this observation the system can be considered as a perturbation of harmonic oscillator. The perturbation method is used to approximate the energy levels of pseudo- Gaussian oscillator. The results are compared with those obtained in the analytic and numeric case.

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.

Gauge-invariant non-spherical metric perturbations of Schwarzschild black-hole spacetimes

International Nuclear Information System (INIS)

Nagar, Alessandro; Rezzolla, Luciano

2005-01-01

The theory of gauge-invariant non-spherical metric perturbations of Schwarzschild black-hole spacetimes is now well established. Yet, as different notations and conventions have been used throughout the years, the literature on the subject is often confusing and sometimes confused. The purpose of this review is to review and collect the relevant expressions related to the Regge-Wheeler and Zerilli equations for the odd and even-parity perturbations of a Schwarzschild spacetime. Special attention is paid to the form they assume in the presence of matter-sources and, for the two most popular conventions in the literature, to the asymptotic expressions and gravitational-wave amplitudes. Besides pointing out some inconsistencies in the literature, the expressions collected here could serve as a quick reference for the calculation of the perturbations of a Schwarzschild black-hole spacetime driven by generic sources and for those approaches in which gravitational waves are extracted from numerically generated spacetimes. (topical review)

Vlasov simulation of the relativistic effect on the breaking of large amplitude plasma waves

International Nuclear Information System (INIS)

Xu Hui; Sheng Zhengming; Zhang Jie

2007-01-01

The influence of relativistic and thermal effects on plasma wave breaking has been studied by solving the coupled Vlasov-Poisson equations. When the relativistic effect is not considered, the wave breaking will not occur, provided the initial perturbation is less than certain value as predicted previously, and the largest amplitude of the plasma wave will decrease with the increase of the initial temperature. When the relativistic effect is considered, wave breaking always occurs during the time evolution, irrespective of the initial perturbation amplitude. Yet the smaller the initial perturbation amplitude is, the longer is the time for wave breaking to occur. With large initial perturbations, wave breaking can always occur with the without the relativistic effect. However, the results are significantly different in the two cases. The thermal effects of electrons decrease the threshold value to initial amplitude for wave breaking and large phase velocity makes the nonlinear phenomenon occur more easily. (authors)

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

On the partitioning method and the perturbation quantum theory - discrete spectra

International Nuclear Information System (INIS)

Logrado, P.G.

1982-05-01

Lower and upper bounds to eigenvalues of the Schroedinger equation H Ψ = E Ψ (H = H 0 + V) and the convergence condition, in Schonberg's perturbation theory, are presented. These results are obtained using the partitioning technique. It is presented for the first time a perturbation treatment obtained when the reference function in the partitioning technique is chosen to be a true eigenfunction Ψ. The convergence condition and upper and lower bounds for the true eigenvalues E are derived in this formulation. The concept of the reaction and wave operators is also discussed. (author)

Second-order perturbations of cosmological fluids: Relativistic effects of pressure, multicomponent, curvature, and rotation

International Nuclear Information System (INIS)

Hwang, Jai-chan; Noh, Hyerim

2007-01-01

We present general relativistic correction terms appearing in Newton's gravity to the second-order perturbations of cosmological fluids. In our previous work we have shown that to the second-order perturbations, the density and velocity perturbation equations of general relativistic zero-pressure, irrotational, single-component fluid in a spatially flat background coincide exactly with the ones known in Newton's theory without using the gravitational potential. We also have shown the effect of gravitational waves to the second order, and pure general relativistic correction terms appearing in the third-order perturbations. Here, we present results of second-order perturbations relaxing all the assumptions made in our previous works. We derive the general relativistic correction terms arising due to (i) pressure, (ii) multicomponent, (iii) background spatial curvature, and (iv) rotation. In the case of multicomponent zero-pressure, irrotational fluids under the flat background, we effectively do not have relativistic correction terms, thus the relativistic equations expressed in terms of density and velocity perturbations again coincide with the Newtonian ones. In the other three cases we generally have pure general relativistic correction terms. In the case of pressure, the relativistic corrections appear even in the level of background and linear perturbation equations. In the presence of background spatial curvature, or rotation, pure relativistic correction terms directly appear in the Newtonian equations of motion of density and velocity perturbations to the second order; to the linear order, without using the gravitational potential (or metric perturbations), we have relativistic/Newtonian correspondences for density and velocity perturbations of a single-component fluid including the rotation even in the presence of background spatial curvature. In the small-scale limit (far inside the horizon), to the second-order, relativistic equations of density and

Primordial non-Gaussianities of gravitational waves in the most general single-field inflation model with second-order field equations.

Science.gov (United States)

Gao, Xian; Kobayashi, Tsutomu; Yamaguchi, Masahide; Yokoyama, Jun'ichi

2011-11-18

We completely clarify the feature of primordial non-Gaussianities of tensor perturbations in the most general single-field inflation model with second-order field equations. It is shown that the most general cubic action for the tensor perturbation h(ij) is composed only of two contributions, one with two spacial derivatives and the other with one time derivative on each h(ij). The former is essentially identical to the cubic term that appears in Einstein gravity and predicts a squeezed shape, while the latter newly appears in the presence of the kinetic coupling to the Einstein tensor and predicts an equilateral shape. Thus, only two shapes appear in the graviton bispectrum of the most general single-field inflation model, which could open a new clue to the identification of inflationary gravitational waves in observations of cosmic microwave background anisotropies as well as direct detection experiments.

Using projector augmented-wave (PAW) formalism inside the density-functional perturbation theory; L'utilisation du formalisme PAW en theorie de la fonctionnelle de la densite perturbee

Energy Technology Data Exchange (ETDEWEB)

Audouze, Ch

2006-07-01

In condensed matter physics, ab-initio simulation allows to get macroscopic quantities (for example equations of state) from microscopic ones, as phonon frequencies which characterize the vibration Eigenmodes of the system. Therefore, one can theoretically predict the behavior of the material at very high pressure conditions, which can be out of reach by experiences. Computations of phonon spectrum are obtained thanks to the linear response theory, where the equations of Density Functional Theory (as the Kohn-Sham model) are perturbed around their fundamental state. The linear response functionality is one of the options included in the ABINIT code, which is an open source package developed in particular by a team of the CEA-DAM (DPTA) and the Catholic University of Louvain-la-Neuve (Belgium). Nevertheless, in spite of using pseudopotentials, computations of phonon spectrum are not tractable for heavy chemical elements, even on massively parallel computers. In order to overcome this difficulty, the linear response theory had to be extended to the PAW (Projector Augmented-Waves) formalism. In this CEA report, we first detail the PAW model, giving to it a more mathematical framework. Then we establish the linear response equations within the PAW formalism, up to the third order derivative of the total energy, for an isolated molecular system and for generic perturbations. Lastly, all these results are specified to the particular case of atom displacements and for perturbations associated to the change of an external potential in which the molecule is set. (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

Second-Order Moller-Plesset Perturbation Theory for Molecular Dirac-Hartree-Fock Wave Functions

Science.gov (United States)

Dyall, Kenneth G.; Arnold, James O. (Technical Monitor)

1994-01-01

Moller-Plesset perturbation theory is developed to second order for a selection of Kramers restricted Dirac-Hartree-Fock closed and open-shell reference wave functions. The open-shell wave functions considered are limited to those with no more than two electrons in open shells, but include the case of a two-configuration SCF reference. Denominator shifts are included in the style of Davidson's OPT2 method. An implementation which uses unordered integrals with labels is presented, and results are given for a few test cases.

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

Dispersion properties of transverse waves in electrically polarized BECs

International Nuclear Information System (INIS)

Andreev, Pavel A; Kuz'menkov, L S

2014-01-01

Further development of the method of quantum hydrodynamics in applications for Bose–Einstein condensates (BECs) is presented. To consider the evolution of polarization direction along with particle movement, we have developed a corresponding set of quantum hydrodynamic equations. It includes equations of the polarization evolution and the polarization-current evolution along with the continuity equation and the Euler equation (the momentum-balance equation). Dispersion properties of the transverse waves, including the electromagnetic waves propagating through the BECs, are considered. To this end, we consider a full set of the Maxwell equations for the description of electromagnetic field dynamics. This approximation gives us the possibility of considering the electromagnetic waves along with the matter waves. We find a splitting of the electromagnetic-wave dispersion on two branches. As a result, we have four solutions, two for the electromagnetic waves and two for the matter waves; the last two are the concentration-polarization waves appearing as a generalization of the Bogoliubov mode. We also find that if the matter wave propagates perpendicular to the external electric field then the dipolar contribution does not disappear (as it follows from our generalization of the Bogoliubov spectrum). A small dipolar frequency shift exists in this case due to the transverse electric field of perturbation. (paper)

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 ...

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.

Born approximation to a perturbative numerical method for the solution of the Schrodinger equation

International Nuclear Information System (INIS)

Adam, Gh.

1978-05-01

A perturbative numerical (PN) method is given for the solution of a regular one-dimensional Cauchy problem arising from the Schroedinger equation. The present method uses a step function approximation for the potential. Global, free of scaling difficulty, forward and backward PN algorithms are derived within first order perturbation theory (Born approximation). A rigorous analysis of the local truncation errors is performed. This shows that the order of accuracy of the method is equal to four. In between the mesh points, the global formula for the wavefunction is accurate within O(h 4 ), while that for the first order derivative is accurate within O(h 3 ). (author)

Effect of non Maxwellian distribution on the dressed electrostatic wave and energy properties

Directory of Open Access Journals (Sweden)

N.F. Abdo

2017-07-01

Full Text Available The investigation of dressed electrostatic and energy ion acoustic solitary waves in a warm plasma composed fluid of ions, Maxwillian positrons and fast nonthermal electrons are elaborated. The plasma system is reduced to KdV equation that obtained using reductive perturbation method. For enlarged amplitude, the higher order perturbed equation is proposed. The positron parameters and nonthermal electron effects on broadband dressed electric field and energy are discussed.

Evolution of weak perturbations in gas-solid suspension with chemical reaction

Energy Technology Data Exchange (ETDEWEB)

Sharypov, O.V. [Russian Academy of Sciences, Novosibirsk (Russian Federation). Inst. of Thermophysics; Novosibirsk State Univ. (Russian Federation); Anufriev, I.S. [Novosibirsk State Univ. (Russian Federation)

2013-07-01

Dynamics of weak finite-amplitude perturbations in two-phase homogeneous medium (gas + solid particles) with non-equilibrium chemical reaction in gas is studied theoretically. Non-linear model of plane perturbation evolution is substantiated. The model takes into account wave-kinetic interaction and dissipation effects, including inter-phase heat and momentum transfer. Conditions for uniform state of the system are analyzed. Non-linear equation describing evolution of plane perturbation is derived under weak dispersion and dissipation effects. The obtained results demonstrate self-organization in the homogeneous system: steady-state periodic structure arises, its period, amplitude and velocity depends on the features of the medium. The dependencies of these parameters on dissipation and chemical kinetics are analyzed.

The Schroedinger equation and canonical perturbation theory

International Nuclear Information System (INIS)

Graffi, S.; Paul, T.

1987-01-01

Let T 0 (ℎ,ω)+εV be the Schroedinger operator corresponding to the classical Hamiltonian H 0 (ω)+εV, where H 0 (ω) is the d-dimensional harmonic oscillator with non-resonant frequencies ω=(ω 1 ..., ω d ) and the potential V(q 1 , ..., q d ) is an entire function of order (d+l) -1 . We prove that the algorithm of classical, canonical perturbation theory can be applied to the Schroedinger equation in the Bargmann representation. As a consequence, each term of the Rayleigh-Schroedinger series near any eigenvalue of T 0 (ℎ,ω) admits a convergent expansion in powers of ℎ of initial point the corresponding term of the classical Birkhoff expansion. Moreover if V is an even polynomial, the above result and the KAM theorem show that all eigenvalues λ n (ℎ,ε) of T 0 +εV such that nℎ coincides with a KAM torus are given, up to order ε ∞ , by a quantization formula which reduces to the Bohr-Sommerfeld one up to first order terms in ℎ. (orig.)