2019/09/01 by Nikolay K. Vitanov, Vitanov, Nikolay K.
Mathematics · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Fractional Differential Equations Solutions #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1909.00330
openalex publication_date 2019/09/01 · openalex created_date 2019/09/12 · openalex updated_date 2026/07/28
We discuss the last version as well as applications of a method for obtaining exact solutions of nonlinear partial differential equations. As this version is based on more than one simple equation we call it Simple Equations Method (SEsM). SEsM contains as particular case the Modified Method of Simplest Equation (MMSE) for the case when we use one simple equation and the solution is searched as power series of the solution of the simple equation. SEsM contains as particular cases many other methodologies for obtaining exact solutions of non-linear partial differential equations. We demonstrate that SEsM can lead to multisoliton solutions of integrable nonlinear partial differential equations and in addition we demonstrate that SEsM keeps the property of the Modified Method of Simplest Equation to lead to exact solutions of nonitegrable nonlinear partial differential equations.