Related papers: A note on solitary waves solutions of classical wa…
Weierstrass's theory is a standard qualitative tool for single degree of freedom equations, used in classical mechanics and in many textbooks. In this Brief Report we show how a simple generalization of this tool makes it possible to…
Unlike the heat equation or the Laplace equation, solutions of the wave equation on general domains have no known stochastic representation. This short note gives a simple solution to this well known problem in arbitrary dimensions. The…
In this paper we study the solitary waves for the coupled Schr\"odinger - Maxwell equations in three-dimensional space. We prove the existence of a sequence of radial solitary waves for these equations with a fixed $L^2$ norm. We study the…
The method of simplest equation is applied for obtaining exact solitary traveling-wave solutions of nonlinear partial differential equations that contain monomials of odd and even grade with respect to participating derivatives. The used…
In this paper, we overview the recent progresses on the lifespan estimates of classical solutions of the initial value problems for nonlinear wave equations in one space dimension. There are mainly two directions of the developments on the…
In this work an extended elliptic function method is proposed and applied to the generalized shallow water wave equation. We systematically investigate to classify new exact travelling wave solutions expressible in terms of quasi-periodic…
We provide the existence and asymptotic description of solitary wave solutions to a class of modified Green-Naghdi systems, modeling the propagation of long surface or internal waves. This class was recently proposed by Duch{\^e}ne, Israwi…
The goal of this work is to determine classes of traveling solitary wave solutions for Lattice Boltzmann schemes by means of an hyperbolic ansatz. It is shown that spurious solitary waves can occur in finite-difference solutions of…
We study the orbital stablity and instability of solitary wave solutions for nonlinear Schr\"odinger equations of derivative type.
A unified treatment for the propagation of classical waves in inhhomogeneous media is proposed. We deal with four kinds of waves, they are the acoustic wave in fluid, the elastic shear wave in two diemnsional solid, and the E- and…
In this paper, we study the lifespan estimates of classical solutions for semilinear wave equations with characteristic weights and compactly supported data in one space dimension. The results include those for weights by time-variable, but…
It is known that there are nonlinear wave equations with localized solitary wave solutions. Some of these solitary waves are stable (with respect to a small perturbation of initial data) and have nonzero spin (nonzero intrinsic angular…
The present paper is a numerical study of the dynamics of solitary wave solutions of the fractional nonlinear Schr\"{o}dinger equation, whose existence was analyzed by the authors in the first part of the project. The computational study…
The present note aims to provide a clear and explicit derivation of the orthonormality condition, and the completeness property of the Volkov wave function. Thus, none of the results are new.
The model we deal with is the mathematical model for mutually penetrating continua one of which is the carrying medium obeying the wave equation whereas the other one is the oscillating inclusion described by the equation for oscillators.…
The travelling wave problem for a particular bidirectional Whitham system modelling surface water waves is under consideration. This system firstly appeared in [Dinvay, Dutykh, Kalisch 2018], where it was numerically shown to be stable and…
In this study we compute numerical traveling wave solutions to a compact version of the Zakharov equation for unidirectional deep-water waves recently derived by Dyachenko & Zakharov (2011) Furthermore, by means of an accurate Fourier-type…
We apply the version of the method of simplest equation called modified method of simplest equation for obtaining exact traveling wave solutions of a class of equations that contain as particular case a nonlinear PDE that models shallow…
This article produces wave equations and constructs traveling wave solutions that are intimately related to Newton's equations of celestial mechanics. The traveling wave solutions are expressed in ``closed form'' in terms of elementary…
A 3D singular integral equation is derived for electromagnetic wave scattering by bodies of arbitrary shape. Its numerical solution by a projection method is outlined.