Related papers: Opportunity of representation of the nonlinear wav…
We introduce a new class of piece-wise quadratic potentials for nonlinear wave equations with a kink solutions. The potentials allow an exact description of the spectral properties for the linearized equation at the kink. This description…
We study heteroclinic standing waves (dark solitons) in discrete nonlinear Schr\"{o}dinger equations with defocussing nonlinearity. Our main result is a quite elementary existence proof for waves with monotone and odd profile, and relies on…
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…
It is well recognized that new types of exact travelling wave solutions to nonlinear partial differential equations can be obtained by modifications of the methods which are in hand. In this study, we extend the class of auxiliary equations…
The Naive Angle Method, used by Geometry Expressions for solving problems which involve only angle constraints, represents a geometrical configuration as a sparse linear system. Linear systems with the same underlying matrix structure…
The purpose of this note is to present a formulation of a given nonlinear ordinary differential equation into an equivalent system of linear ordinary differential equations. It is evident that the easiness of a such procedure would be able…
There are important differences between the nonrelativistic and relativistic description of electron beams. The orbital angular momentum quantum number cannot be used to specify the wave functions in the relativistic case. In this Letter we…
Generalized action invariants are identified for various models of drift wave turbulence in the presence of the mean shear flow. It is shown that the wave kinetic equation describing the interaction of the small scale turbulence and large…
We use variable transformation from the real line to finite or semi-infinite spaces where we expand the regular solution of the 1D time-independent Schrodinger equation in terms of square integrable bases. We also require that the basis…
We consider a system of nonlinear equations which can be reduced to a degenerate parabolic equation. In the case $x\in\bR^2$ we obtained necessary conditions for the existence of a weakly singular solution of heat wave type…
We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential…
We show that the self-interactions present in the effective field theory formulation of general relativity can couple gravitational wave modes and generate nonclassical states. The output of gravitational nonlinear processes can also be…
We propose a simple algebraic method for generating classes of traveling wave solutions for a variety of partial differential equations of current interest in nonlinear science. This procedure applies equally well to equations which may or…
Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding polynomial solutions of a partial differential equations is…
In this article we shall go over recent work in proving dispersive and Strichartz estimates for the Dirichlet-wave equation. We shall discuss applications to existence questions outside of obstacles and discuss open problems.
The concept of the derivative-dependent functional separable solution, as a generalization to the functional separable solution, is proposed. As an application, it is used to discuss the generalized nonlinear diffusion equations based on…
Global smooth solutions to the initial value problem for systems of nonlinear wave equations with multiple propagation speeds will be constructed in the case of small initial data and nonlinearities satisfying the null condition.
We describe a variant of the dressing method giving alternative representation of multidimensional nonlinear PDE as a system of Integro-Differential Equations (IDEs) for spectral and dressing functions. In particular, it becomes single…
In the present work, we attempt a brief summary of various areas where nonlinear waves have been emerging in the phenomenology of lattice dynamical systems. These areas include nonlinear optics, atomic physics, mechanical systems,…
A novel mathematical nonlinear theory of surface gravity waves in deep water is presented, in which analytical analysis of the classical nonlinear equations of fluid dynamics is performed under less restrictive assumptions than those…