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

2019/08/19 by Nikolay K. Vitanov, Vitanov, Nikolay K., Zlatinka I. Dimitrova +1 · 1 citation
Chemistry · Materials Science · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #Chemical and Physical Properties of Materials #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Scientific Research and Discoveries

paper · pdf · doi:10.48550/arxiv.1908.07459

openalex publication_date 2019/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• The Simple Equations Method (SEsM) and the use of exponential functions for obtaining simple and multisoliton solutions of some nonlinear partial differential equations

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