Exponential rational function method for solving nonlinear equations arising in various physical models

•Exact solutions of nonlinear evolution equations plays an important role in nonlinear phenomena.•Exact solutions are obtained by the exponential rational function method.•The existence of soliton-type solutions is important because of their potential application in many physical wave phenomena.•It is shown that the proposed algorithm is effective and can be used for many nonlinear equations in mathematical physics.•This approach can also be applied to other nonlinear evolution equations.

In this paper, we explore new applications of the exponential rational function method to the scalar Qiao equation and the Kuramoto-Sivashinsky equation. The obtained solutions may be of significance for the explanation of some practical physical problems. The method is very suitable, easy and effective handling of the solution process of nonlinear equations.