Periodic Travelling Wave Solutions of Discrete Nonlinear Schrödinger Equations

Periodic Wave Shock solutions of Burgers equations

In this paper we investigate the exact peroidic wave shock solutions of the Burgers equations. Our purpose is to describe the asymptotic behavior of the solution in the cauchy problem for viscid equation with small parametr ε and to discuss in particular the case of periodic wave shock. We show that the solution of this problem approaches the shock type solution for the cauchy problem of the in...

Travelling Wave Solutions for the KdV-Burgers-Kuramoto and Nonlinear Schrödinger Equations Which Describe Pseudospherical Surfaces

Periodic Solutions of Nonlinear Wave Equations

where f is a given continuous function in R 3 and f is T-periodic in t and s. Periodic solutions of nonlinear hyperbolic partial differential equations have been studied extensively in the recent years [1, 6, 7, 8, 9, 10, 11, 12, 13, 14]. The two approaches that have been used are: (i) reduction to an alternative problem and (ii) the Galerkin method and passage to the limit through a sequence o...

Exact Travelling Wave Solutions of Some Nonlinear Nonlocal Evolutionary Equations

Direct algebraic method of obtaining exact solutions to nonlinear PDE’s is applied to certain set of nonlinear nonlocal evolutionary equations, including nonlinear telegraph equation, hyperbolic generalization of Burgers equation and some spatially nonlocal hydrodynamic-type model. Special attention is paid to the construction of the kink-like and soliton-like solutions.

Exact travelling wave solutions for some complex nonlinear partial differential equations

This paper reflects the implementation of a reliable technique which is called $left(frac{G'}{G}right)$-expansion  ethod for  constructing exact travelling wave solutions of nonlinear partial  differential equations. The proposed algorithm has been successfully tested on two two selected equations, the balance numbers of which are not positive integers namely Kundu-Eckhaus equation and  Derivat...