Dynamics of solitons of the nonlinear dispersion Drinfel'd-Sokolov system by ansatz method and He's varitional principle

Abstract

In this article, the exact-special solutions of the nonlinear dispersion Drinfel'd-Sokolov (shortly $D(m,n)$) system are analyzed. We use the ansatz approach and the He's variational principle for the mentioned equation. The general formulae for the compactons, solitary patterns, solitons and periodic solutions are acquired. These types of solutions are useful and attractive for clarifying some types of nonlinear physical phenomena. These two methods will be used to carry out the integration.