相关论文: Factorization of damped wave equations with cubic …

Scalar conservation laws with non-convex fluxes have shock wave solutions that violate the Lax entropy condition. In this paper, such solutions are selected by showing that some of them have corresponding traveling waves for the equation…

The modification of simplest equation method to look for exact solutions of nonlinear partial differential equations is presented. Using this method we obtain exact solutions of generalized Korteweg-de Vries equation with cubic source and…

In the dynamics generated by the suspension bridge equation, traveling waves are an essential feature. The existing literature focuses primarily on the idealized one-dimensional case, while traveling structures in two spatial dimensions…

This paper reports results on the classification of traveling wave solutions, including nonnegative weak sense, in the spatial 1D degenerate parabolic equation. These are obtained through dynamical systems theory and geometric approaches…

The finite element method (FEM) is applied to obtain numerical solutions to a recently derived nonlinear equation for the shallow water wave problem. A weak formulation and the Petrov-Galerkin method are used. It is shown that the FEM gives…

For both cubic and quintic nonlinearities of the one-dimensional complex Ginzburg-Landau evolution equation, we prove by a theorem of Eremenko the finiteness of the number of traveling waves whose squared modulus has only poles in the…

Damped mechanical systems with various forms of damping are quantized using the path integral formalism. In particular, we obtain the path integral kernel for the linearly damped harmonic oscillator and a particle in a uniform gravitational…

We use a simple method that leads to the integrals involved in obtaining the traveling wave solutions of wave equations with one and two exponential nonlinearities. When the constant term in the integrand is zero, implicit solutions in…

This paper is devoted to the investigation of long-time behaviour of solutions to wave equations with quadratic nonlinearity and cubic Dirac equations with Hartree-type nonlinearity. We consider the nonlinearity here with enough simplicity…

We study traveling wave solutions of the nonlinear variational wave equation. In particular, we show how to obtain global, bounded, weak traveling wave solutions from local, classical ones. The resulting waves consist of monotone and…

In this paper we prove the existence of finite traveling-wave type solutions to the nonlinear double degenerate parabolic equation of turbulent filtration with absorption.

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…

We study processes with unstable particles in intermediate time-like states. It is shown that the amplitudes squared of such processes factor exactly in the framework of the model of unstable particles with continuous masses. Decay widths…

A subset of traveling wave solutions of the quintic complex Ginzburg-Landau equation (QCGLE) is presented in compact form. The approach consists of the following parts. - Reduction of the QCGLE to a system of two ordinary differential…

We study the steady uniphase and multiphase solutions of the discretized nonlinear damped wave equation.Conditions for the stability abd instability of the steady solutions are given;in the instability case the linear stable and unstable…

We derive sharp decay estimates and prove holomorphic extensions for the solutions of a class of semilinear nonlocal elliptic equations with linear part given by a sum of Fourier multipliers with finitely smooth symbols at the origin.…

A set of travelling wave solutions to a hyperbolic generalization of the convection-reaction-diffusion is studied by the methods of local nonlinear alnalysis and numerical simulation. Special attention is paid to displaying appearance of…

We present a new technique for constructing solutions of quasilinear systems of first-order partial differential equations, in particular inhomogeneous ones. A generalization of the Riemann invariants method to the case of inhomogeneous…

This paper deals with the inverse problem of recovering an arbitrary number of fractional damping terms in a wave equation. We develop several approaches on uniqueness and reconstruction, some of them relying on Tauberian theorems on the…

It is shown how the Canonical Function approach can be used to obtain accurate solutions for the distorted wave problem taking account of direct static and polarisation potentials and exact non-local exchange. Calculations are made for…