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

简单方程法（SEsM）的五个具体案例

Five Specific Cases of the Simple Equations Method (SEsM)

本文讨论简单方程法（SEsM）用于求解非线性偏微分方程，并证明六种已知方法是其具体案例。

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

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…

简单方程法（SEsM）在获取非线性偏微分方程精确解中的几个应用实例

Several Examples of Application of the Simple Equations Method (SEsM) for Obtaining Exact Solutions of Nonlinear PDEs

本文应用简单方程法（SEsM）获取非线性微分方程的精确解，并通过多个实例说明了在SEsM算法中使用复合函数导数的结果。

Simple Equations methodology (SEsM) for searching of multisolitons and other exact solutions of nonlinear partial differential equations

We discuss a version the methodology for obtaining exact solutions of nonlinear partial differential equations based on the possibility for use of: (i) more than one simplest equation; (ii) relationship that contains as particular cases the relationship used by Hirota \cite{hirota} and the relationship used in the previous version of the methodology; (iii) transformation of the solution that contains as particular case the possibility of use of the Painleve expansion; (iv) more than one balance equation. The discussed version of the methodology allows: (i) obtaining multi-soliton solutions of …

Solitary wave solutions for nonlinear partial differential equations containing monomials of odd and even grades with respect to participating derivatives

We apply the method of simplest equation for obtaining exact solitary traveling-wave solutions of nonlinear partial differential equations that contain monomials of odd and even grade with respect to participating derivatives. We consider first the general case of presence of monomials of the both (odd and even) grades and then turn to the two particular cases of nonlinear equations that contain only monomials of odd grade or only monomials of even grade. The methodology is illustrated by numerous examples.