On an exact classical wave solution of the Einstein equations

The J. Scherk and J. H. Schwarz generalization of a Peres solution is shown to be the Peres solution in a different system of coordinates.     

矢量波动方程的球面波解

利用线性变换的方法，将球坐标下矢量波动方程解的形式L、M和N变换为其他多种形式．     

On Nth-order rogue wave solution to the generalized nonlinear Schrödinger equation

In this Letter, the generalized nonlinear Schrödinger (GNLS) equation is investigated by Darboux matrix method. A generalized Darboux transformation (DT) of the GNLS equation is constructed with the help of the gauge transformation for an Ablowitz–Kaup–Newell–Segur (AKNS) type GNLS spectral problem, from which a unified formula of Nth-order rogue wave solution to the GNLS equation is given. In particular, the first and second-order rogue wave solutions to the GNLS equation are explicitly illustrated through some figures.     

On Nth-order rogue wave solution to nonlinear coupled dispersionless evolution equations

The generalized Darboux transformation is applied to obtain Nth-order rogue wave solution of nonlinear coupled dispersionless evolution equations (NLCDEE). In particular, the interesting structures for these solutions from first to third order rogue wave are shown.     

On the non-existence of hydrodynamic solution of surface plasmons at the bimetallic interface

It is shown that for an abrupt bimetallic interface a hydrodynamic solution for interface plasmons does not exist. It appears that this result is valid irrespective of the choice of of the additional boundary condition, thereby suggesting a careful look at the use of usual hydrodynamic equations for a bimetallic interface.     

On the origin of nonequilibrium radiation from iodine molecules at the shock wave front

The direct simulation Monte Carlo (DSMC) method is used for modeling the problem on the shock wave front in the 0.7%I₂-99.3%He mixture for a shock wave Mach number of 4.85. The choice of this system is due to the fact that intense radiation peaks have been observed experimentally precisely in such systems and it has been convincingly proven that this effect is induced by high-energy collisions between I₂ molecules. The results of simulation provide additional sound arguments in favor of the conclusion that the translational nonequilibrium state at the shock wave front in a light gas with a small admixture of heavy nonreacting molecules may cause the experimentally observed nonequilibrium radiation peaks.     

Numerical solution of the conformable space-time fractional wave equation

In this paper, an efficient numerical method is considered for solving space-time fractional wave equation. The fractional derivatives are described in the conformable sense. The method is based on shifted Chebyshev polynomials of the second kind. Unknown function is written as Chebyshev series with the N term. The space-time fractional wave equation is reduced to a system of ordinary differential equations by using the properties of Chebyshev polynomials. The finite difference method is applied to solve this system of equations. Numerical results are provided to verify the accuracy and efficiency of the proposed approach.     

Symmetry groups and spiral wave solution of a wave propagation equation

We study a third-order nonlinear evolution equation, which can be transformed to the modified KdV equation, using the Lie symmetry method. The Lie point symmetries and the one-dimensional optimal system of the symmetry algebras are determined. Those symmetries are some types of nonlocal symmetries or hidden symmetries of the modified KdV equation. The group-invariant solutions, particularly the travelling wave and spiral wave solutions, are discussed in detail, and a type of spiral wave solution which is smooth in the origin is obtained.     

黏性水波振荡型行波解的存在性

利用追赶法技巧,研究了倾度为常数的宽矩形通道中黏性水波振荡型行波解的存在性,证明了当黏性系数、摩擦系数、倾度和高度比满足一定关系时,存在唯一的振荡型行波解.由于解析求解的困难,通过数值计算,给出了部分结果,最后进一步讨论了可能存在的振荡型行波解的结构. 关键词： 追赶法 黏性水波 振荡型行波解     

On the impossible pilot wave

The strange story of the von Neumann impossibility proof is recalled, and the even stranger story of later impossibility proofs, and how the impossible was done by de Broglie and Bohm. Morals are drawn.     

Rational homoclinic solution and rogue wave solution for the coupled long-wave–short-wave system

In this paper, a rational homoclinic solution is obtained via the classical homoclinic solution for the coupled long-wave–short-wave system. Based on the structures of ratinal homoclinic solution, the characteristics of homoclinic solution are discussed which might provide us with useful information on the dynamics of the relevant physical fields.     

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.     

On the detection of objects buried at a shallow depth using seismic wave reflections

This paper concerns the detection of shallow (of the order 1 m) buried objects using seismic excitation. Time-extended signals are used to generate a compressional wave using a shaker attached to the ground. The wave propagates through the ground, reflects off a buried object and is captured by an array of geophones on the surface. The envelopes of the cross-correlation functions between the measured ground velocities and the excitation signal are calculated and summed to generate a cross-sectional image of the ground. The wide cross-correlation peaks caused by high ground attenuation are partially compensated for by using the generalized cross-correlation function called the phase transform. Simple simulations are conducted to demonstrate the method, and some field experiments have been carried out aimed at the detection of a buried concrete pipe. In the experiments the pipe could be detected using the method proposed, with experimental and simulated data producing good agreement.     

The novel multi-solitary wave solution to the fifth-order KdV equation

By using Hirota‘s method, the novel multi-solitary wave solutions to the fifth-order KdV equation are obtained. Furthermore, various new solitary wave solutions are also derived by a reconstructed bilinear Bǎcklund transformation.     

On the theory of wave packets

In this paper we discuss some aspects of the theory of wave packets. We consider a popular noncovariant Gaussian model used in various applications and show that it predicts too slow a longitudinal dispersion rate for relativistic particles. We revise this approach by considering a covariant model of Gaussian wave packets, and examine our results by inspecting a wave packet of arbitrary form. A general formula for the time dependence of the dispersion of a wave packet of arbitrary form is found. Finally, we give a transparent interpretation of the disappearance of the wave function over time due to the dispersion—a feature often considered undesirable, but which is unavoidable for wave packets. We find, starting from simple examples, proceeding with their generalizations and finally by considering the continuity equation, that the integral over time of both the flux and probability densities are asymptotically proportional to the factor 1/|x|² in the rest frame of the wave packet, just as in the case of an ensemble of classical particles.     

On the wave function of the universe

A discussion of the wave function for an isotropic universe is given. In order to alleviate that wave function from some of the quantum gravity difficulties, a logarithmic factor $\text{1 ? ln(}\text{R}\text{R}{}_0\text{)}$ is introduced in the gravitational action integral. The discussion is extended to the primordial Coleman-Weinberg scenario.     

The reference wave solution for a two-frequency wave propagating in a random medium

In this work a new reference wave method for solving parabolic-type equations is proposed. The performance of the method is demonstrated by applying it to the equation governing the propagation of the two-frequency mutual coherence function in a random medium. An analytic solution is presented for arbitrary correlation properties of the medium. It is shown that when approximating the transverse structure function of the medium by a quadratic form, the solution reduces to the exact result derived previously. Extensions to more general types of media are considered.