Methods of judging shape of solitary wave and solution formulae for some evolution equations with nonlinear terms of high order

Abstract

In this paper, we present several methods of judging shape of the solitary wave and solution formulae for some nonlinear evolution equations by means of Lienard equations. Then, using the judgement methods and solution formulae, we obtain solutions of the solitary wave for some of important nonlinear evolution equations, which include generalized modified Boussinesq, generalized nonlinear wave, generalized Fisher, generalized Klein–Gordon and generalized Zakharov equations. Some new solitary-wave solutions are found for the equations.