Traveling wave solutions of the generalized Rosenau–Kawahara-RLW equation via the sine–cosine method and a generalized auxiliary equation method

Abstract

Abstract In this paper, we have approached a complicated nonlinear wave equation which links the Rosenau–Kawahara equation to the regularized long wave (RLW) equation. Taking advantages from the sine–cosine method as well as from the generalized auxiliary equation method, we have successfully reached to three types of traveling wave solutions: periodic, hyperbolic and exponential ones. Our results do constitute themselves as a challenge to apply the mentioned techniques in order to solve other generalized dynamical models, for example, the ones which involve phenomena such as a fully nonlinear dispersion and a fully nonlinear convection.