Simple equations method (SEsM) and some of its numerous particular cases

TL;DR

The paper introduces the Simple Equations Method (SEsM), a versatile approach for solving nonlinear partial differential equations by representing solutions through simpler equations, unifying many existing methods.

Contribution

It presents SEsM as a general framework that encompasses various known solution methods for differential equations, offering a unified approach.

Findings

SEsM can derive solutions using simple equations.

It includes methods like G'/G, Exp-function, and Tanh as special cases.

SEsM unifies multiple solution techniques into one framework.

Abstract

We discuss a new version of a method for obtaining exact solutions of nonlinear partial differential equations. We call this method the Simple Equations Method (SEsM). The method is based on representation of the searched solution as function of solutions of one or several simple equations. We show that SEsM contains as particular case the Modified Method of Simplest Equation, G'/G - method, Exp-function method, Tanh-method and the method of Fourier series for obtaining exact and approximate solutions of linear differential equations. These methods are only a small part of the large amount of methods that are particular cases of the methodology of SEsM.