Newly developed analytical method and its applications of some mathematical models

Abstract

This paper presents a newly developed method, namely, the rational sine-Gordon expansion method to find novel exact solutions to nonlinear differential equations. This method is based on the sine-Gordon expansion method. To generalize the approach, we utilize the ansatz, which is a rational function as different to a polynomial function. In this way, we have more general wave solutions for nonlinear dynamic systems. We apply this method to the (2 + 1)-dimensional conformable Zakharov-Kuznetsov modified equal width (ZK-MEW) equation and the modified regularized long wave (MRLW) equation. Some new solutions are reported. Consequently, we submit the new soliton solutions to the literature.