Exact solitary wave and quasi-periodic wave solutions of the KdV-Sawada-Kotera-Ramani equation

Abstract

In this paper we derive new exact solitary wave solutions and quasi-periodic traveling wave solutions of the KdV-Sawada-Kotera-Ramani equation by using a method which we introduce here for the first time. Firstly, we reduce the associated fourth-order nonlinear ordinary differential equation (ODE) into a solvable first-order nonlinear ODE to obtain new exact traveling wave solutions, including the solitary wave and periodic solutions. Furthermore, using the new method we derive the quasi-periodic wave solutions of this equation by assuming that the solutions of the corresponding higher-order ODE are the sum of the solutions of two solvable first-order nonlinear ODEs. This new method can be used to investigate the exact traveling wave solutions and quasi-periodic wave solutions of a general class of higher-order wave equations.