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

TL;DR

This paper demonstrates the application of the Simple Equations Method (SEsM) to find exact solutions of nonlinear PDEs through several illustrative examples involving derivatives of composite functions.

Contribution

It introduces and illustrates the use of derivatives of composite functions within SEsM for solving nonlinear differential equations.

Findings

SEsM successfully finds exact solutions for various nonlinear PDEs

Composite function derivatives are effectively incorporated into SEsM

The method enhances the solution process for complex nonlinear equations

Abstract

We apply the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear differential equations. We discuss several examples with goal to illustrate the results from the use of derivatives of composite functions in the algorithm of SEsM. The discussed examples contain derivatives of functions which are composite functions of solutions of two simple equations.