New exact solutions for Kudryashov–Sinelshchikov equation

Abstract

In this paper, we firstly change the auxiliary second order ordinary differential equation in the G′G-polynomial expansion method to the Riccati equation. By solving the Riccati equation, we obtain more exact solutions to the auxiliary equation and thus obtain more new exact solutions to the Kudryashov–Sinelshchikov equation, which mainly include three types of solutions with parameters: hyperbolic function traveling wave solutions, trigonometric function traveling wave solutions, and rational function traveling wave solutions. At last, some examples and figures are given to demonstrate the solutions.