A Simplification for Exp-Function Method When the Balanced Nonlinear Term Is a Certain Product

Abstract

The Exp-function method plays an important role in searching for analytic solutions of many nonlinear differential equations. In this paper, we prove that the balancing procedure in the method is unnecessary when the balanced nonlinear term is a product of the dependent variable under consideration and its derivatives. And in this case, the ansatz of the method can be simplified to be with less parameters so as to be easy to calculate.

Exact Solutions for Nonlinear Wave Equations by the Exp-Function Method

“…By some mathematical software, the solution process is extremely simple and abundant solutions are predicted [19][20][21]. The exp-function method is a universal tool for nonlinear equations and can be easily extended to fractional calculus [22][23][24][25][26][27].…”