Application of the improved F -expansion method with Riccati equation to find the exact solution of the nonlinear evolution equations

http://dx.doi.org/10.1016/j.joems.2016.03.008

Abstract

In this article, we pay attention to the analytical method named, the improved F -
expansion method combined with Riccati equation for finding the exact traveling wave solutions of the Benney–Luke equation and the Phi-4 equation. By means of this method we have explored three classes of explicit solutions-hyperbolic, trigonometric and rational solutions with some free parame-ters. When the parameters are taken as special values, the solitary wave solutions are originated from the traveling wave solutions. Our outcomes disclose that this method is very active and forthright way of formulating the exact solutions of nonlinear evolution equations arising in mathematical physics
and engineering.
Journal of the Egyptian Mathematical Society
Volume 25, Issue 1
2017
Pages 13-18

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