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

R Soc Open Sci. 2014 Oct 8;1(2):140038. doi: 10.1098/rsos.140038. eCollection 2014 Oct.

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.

Keywords: NLEEs; exact solution; improved -expansion method; modified Benjamin–Bona–Mahony equation; modified Korteweg-de Vries equation.