A note on improved F-expansion method combined with Riccati equation applied to nonlinear evolution equations.

Md Shafiqul Islam,Antonio Mastroberardino,M Ali Akbar,Kamruzzaman Khan

doi:10.1098/rsos.140038

Abstract

The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin–Bona–Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering.

Highlights

SummaryThe purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations
Nonlinear evolution equations (NLEEs) are widely used to describe many important phenomena and dynamical processes in mathematical physics and engineering
The investigation of exact solutions of NLEEs plays an important role in the study of these physical phenomena

Summary

The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin–Bona–Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering

Introduction

Algorithm of improved F-expansion method

Applications

Graphical representation of the obtained solutions

Conclusion