Simple equations method (SEsM) and its connection with the inverse scattering transform method

Abstract

We discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations. We show that a particular case of SEsM can be used in order to reproduce the methodology of the Inverse Scattering Transform Method for the case of the Burgers equation and Korteweg - de Vries equation. This particular case is connected to use of specific case of Step. 2 of SEsM: reprentation of the solution of the solved nonlinear partial differential equation as expansion as power series containing powers of a ”small” parameter є, solving the differential equations arrising from this representation by means of Fourier series and transition from the obtained solution for small values of є to solution for arbitrary finite values of є.