Simple equations method (SEsM) and its particular cases: Hirota method

Abstract

We discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations. We show that the Hirota method is particular case of SEsM for specific form of the function from the Step. 2 of SEsM and for simple equations from the kind of differential equation for exponential function. We illustrate the methodology by obtaining the three-soliton solution of the Korteweg - de Vries equation, two soliton solution of the nonlinear Schrodinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials.