title: A note on improved F-expansion method combined with Riccati equation applied to nonlinear evolution equations.
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.
authors.affiliation: Department of Mathematics , Pabna University of Science and Technology , Pabna 6600, Bangladesh.
authors.forename: Md Shafiqul
authors.initials: MS
authors.lastname: Islam
authors.affiliation: Department of Mathematics , Pabna University of Science and Technology , Pabna 6600, Bangladesh.
authors.forename: Kamruzzaman
authors.identifier: 0000-0002-4531-288X
authors.initials: K
authors.lastname: Khan
authors.affiliation: Department of Applied Mathematics , University of Rajshahi , Rajshahi 6205, Bangladesh.
authors.forename: M Ali
authors.initials: MA
authors.lastname: Akbar
authors.affiliation: School of Science, Penn State Erie, The Behrend College , Erie, PA 16563, USA.
authors.forename: Antonio
authors.initials: A
authors.lastname: Mastroberardino
keywords: NLEEs; exact solution; improved -expansion method; modified Benjamin–Bona–Mahony equation; modified Korteweg-de Vries equation