New solitons and periodic wave solutions for the dispersive long wave equations

We make use of Jacobi elliptic functions to construct periodic wave solutions for the dispersive long wave equations. In the limit cases the multiple soliton solutions are also obtained. The properties of some periodic and soliton solutions for the dispersive long wave equations are shown by some figures. As a result, we can successfully obtain the solitary wave solutions that can be found by the previous work.     

Time-frequency analysis of the dispersive Rayleigh wave in stratified media

The dispersive characteristic of the Rayleigh wave propagating in a stratified media was analyzed by a time-frequency analysis method, the Reassignment of Smooth Pseudo-Wigner Ville Distribution (RSPWVD). Theoretical simulations and experiments were implemented for a homogeneous half-space and a two-layered half-space. It is indicated that the group velocity dispersion curves in different frequency ranges obtained by experimental result are all corresponding to the dominant modes in their surface displacement amplitudes. Such a mode identification of the multi-mode Rayleigh waves is required in inversing the medium parameters.     

Modulational instability and envelope solutions of nonlinear dispersive wave equations

The nonlinear Schrödinger equation describing the evolution of the plane wave solutions of the Hirota equation and of the Boussinesq equation are obtained. The conditions for modulational instability and the localised stationary solutions are derived.     

The wave equation with viscoelastic attenuation and its application in problems of shallow-sea acoustics

A suitable tool for the simulation of low frequency acoustic pulse signals propagating in a shallow sea is the numerical integration of the nonstationary wave equation. The main feature of such simulation problems is that in this case the sound waves propagate in the geoacoustic waveguide formed by the upper layers of the bottom and the water column. By this reason, the correct dependence of the attenuation of sound waves in the bottom on their frequency must be taken into account. In this paper we obtain an integro-differential equation for the sound waves in the viscoelastic fluid, which allows to simulate the arbitrary dependence of acoustic wave attenuation on frequency in the time domain computations. The procedure of numerical solution of this equation based on its approximation by a system of differential equations is then considered and the methods of artificial limitation of computational domain are described. We also construct a simple finite-difference scheme for the proposed equation suitable for the numerical solution of nonstationary problems arising in the shallow-sea acoustics.     

New multi—soliton solutions and travelling wave solutions of the dispersive long—wave equations

Using the extended homogeneous balance method,the (1 1)-dimensional dispersive long-wave equations have been solved.Starting from the homogeneous balance method,we have obtained a nonlinear transformation for simplifying a dispersive long-wave equation into a linear partial differential equation.Usually,we can obtain only a type of soliton-like solution.In this paper,we have further found some new multi-soliton solutions and exact travelling solutions of the dispersive long-wave equations from the linear partial equation.     

各向异性黏弹性介质伪谱法波场模拟

当地震信号通过复杂地球介质时，地层除了表现为各向异性，还表现为内在的黏弹性特征 因此，为准确描述地震波在地球介质中的传播特征，理想的地球介质模型应该能够模拟岩石 的各向异性特征和衰减特征.给出了各向异性黏弹性介质模型的波动方程，推导了伪谱法波场正演模拟的递推公式，并利用伪谱法实现了地震波波场数值模拟.表明了该介质模型中地 震波场特征与各向异性主轴方位和介质的黏滞性参数之间的关系. 关键词： 黏弹性 各向异性 伪谱法     

On the velocity of propagation of a frequency-modulated wave packet in a dispersive absorbing medium

It is shown that the velocity of propagation of a frequency-modulated wave packet through a strongly dispersive absorbing medium can be significantly different from (either higher or lower than) that of a non-frequency-modulated wave packet. This difference is attributed to the absorption dispersion of the medium. The easiest way to take the absorption dispersion into account is to use the formalism of the complex group velocity of a wave packet. This paper considers the propagation of a linear frequency-modulated wave packet, whose carrier frequency is close to the frequency of a spectral absorption line of the medium.     

New explicit and exact travelling wave solutions for a system of dispersive long wave equations

A method to construct the new exact solutions of nonlinear partial differential equations (NLPDEs) in a unified way is presented, which is named an improved sine-cosine method. This method is more powerful than the sine-cosine method. Systems of dispersive long wave equations in (1+1) and (2+1) dimensions are chosen to illustrate the method and several types of explicit and exact travelling wave solutions are obtained. These solutions contain Wang's results and other types of solitary wave solutions and new solutions. The method presented here is general and can also be applied to solve more systems of nonlinear partial differential equations, such as the coupled KdV equations.     

Path integral solution of the time-domain progressive wave equation and wave propagation in random media

A time-domain progressive wave equation is derived from the usual linear acoustic wave equation, and it is shown that the solution to this new equation can be expressed as a Feynman path integral. This path integral representation is used to derive the time-dependent statistics of acoustic fields propagating through random media.     

Self-focusing of wave packets and envelope shock formation in nonlinear dispersive media

The self-action of three-dimensional wave packets is analyzed analytically and numerically under the conditions of competing diffraction, cubic nonlinearity, and nonlinear dispersion (dependence of group velocity on wave amplitude). A qualitative analysis of pulse evolution is performed by the moment method to find a sufficient condition for self-focusing. Self-action effects in an electromagnetically induced transparency medium (without cubic nonlinearity) are analyzed numerically. It is shown that the self-focusing of a wave packet is accompanied by self-steepening of the longitudinal profile and envelope shock formation. The possibility of envelope shock formation is also demonstrated for self-focusing wave packets propagating in a normally dispersive medium.     

色散长波方程和变形色散水波方程特殊形状的多孤子解

进一步拓广使用齐次平衡法并对关键的操作步骤进行了改进,从而简便地求出了色散长波方程和变形色散水波方程的一种新的特殊形状的多孤子解。而张解放等得到的多孤子解是本文结果的特殊情况 关键词： 齐次平衡法 特殊形状的多孤子解 色散长波方程 变形色散水波方程     

Pseudo-Hermiticity and electromagnetic wave propagation: The case of anisotropic and lossy media

Pseudo-Hermitian operators can be used in modeling electromagnetic wave propagation in stationary lossless media. We extend this method to a class of non-dispersive anisotropic media that may display loss or gain. We explore three concrete models to demonstrate the utility of our general results and reveal the physical meaning of pseudo-Hermiticity and quasi-Hermiticity of the relevant wave operator. In particular, we consider a uniaxial model where this operator is not diagonalizable. This implies left-handedness of the medium in the sense that only clockwise circularly polarized plane-wave solutions are bounded functions of time.     

Dynamics of the wave packet in a tunnel-coupled structure consisting of amplifying right-handed and absorbing left-handed media

The dynamics of forward and backward waves in the tunnel-coupled waveguide structure that consists of materials with different signs of real and imaginary parts of refractive indices is analyzed. The expressions for the amplitudes of propagating waves and reflection and transmission coefficients are derived. It is demonstrated that such a structure can be used as a slow-wave structure whose parameters can be controlled using an external magnetic field. The absence of the spontaneous generation of the radiation that propagates in the structure is also demonstrated for the given effective gain, phase mismatch of the interacting modes, and waveguide length.     

Differential operators in terms of Clebsch-Gordon (C-G) coefficients and the wave equation of massless tensor fields

The quantum theory of angular momentum affords a treatment of tensors and vectors in a spherical basis. By using this theory we define the tensor differential operators: divergence, curl and gradient which act on a tensor of any rank, in terms of C-G coefficients. With these definitions we obtain a matrix representation and useful properties for those operators. An interesting application of this formalism is to find the wave equation of a tensor of any rank in a linear theory. This provides a new common way to look at the wave equations associated with both Maxwell's equations and the Maxwell-like equations for the linearized Weyl curvature tensor in gravitoelectromagnetism describing gravitational radiation on a Minkowski spacetime background.     

Stokes parameters representation of the light propagation equations in inhomogeneous anisotropic,optically active media

A simple expression is obtained by using the Stokes parameters and transforming the light propagation equations derived by the authors in a weakly inhomogeneous anisotropic active medium. By applying the transformation to photoelasticity it is shown that Aben's equations reduce to $\text{?S/?x}{}_3\text{= Ω × S}$, where S is the polarization vector propagating through the photoelastic medium, x₃ is the distance traveled along the propagation direction and $\text{Ω = (C(σ}{}_{11}\text{? σ}{}_{22}\text{) 2Cσ}{}_{12}\text{0)(σ}{}_{\mathrm{jp}}$, stress tensor components: C, constant), Ω is a vector representing the stress-induced optical properties of the medium which influence the polarization vector. On the basis of the expression obtained it will be convenient to evaluate a stress tensor field in a photoelastic model by measuring the Stokes parameters.     

Modified path integrals and complex Monte Carlo method in the statistical theory of wave propagation in dispersive media

A new representation of the Green function of a wave equation is developed as modified path integrals. The mean-squares value of the wavefield is calculated by the complex Monte Carlo method of a layer of chaotically distributed three-dimensional scatterers with a random scatter of permittivity. Collective resonance events in wave scattering have been detected.