Discussion on exp-function method and modified method of simplest equation

TL;DR

This paper explores the connection between the exp-function method and the modified method of simplest equation, generalizing the ansatz and applying it to find exact solutions for nonlinear PDEs related to water wave propagation.

Contribution

It introduces a generalized exp-function ansatz based on the modified method of simplest equation and demonstrates its application to nonlinear PDEs modeling water waves.

Findings

Derived exact solutions for specific nonlinear PDEs

Established the relation between two solution methods

Extended the applicability of the exp-function method

Abstract

We discuss the relation between the modified method of simplest equation and the exp-function method. First on the basis of our experience from the application of the method of simplest equation we generalize the exp-function ansatz. Then we apply the ansatz for obtaining exact solutions for members of a class of nonlinear PDEs which contains as particular cases several nonlinear PDEs that model the propagation of water waves.