Application of the Kudryashov Method for Finding Exact Solutions of the Schamel – Kawahara Equation

Recently, motivated by the interest in the problems of nonlinear dynamics of cylindrical shells, A. I. Zemlyanukhin et al. (Nonlinear Dyn, 98, 185–194, 2019) established the so-called Schamel – Kawahara equation (SKE). The SKE generalizes the well-known nonlinear Schamel equation that arises in plasma physics problems, by adding the high-order dispersive terms from the Kawahara equation. This article presents families of new solutions to the Schamel – Kawahara model using the Kudryashov method. By performing the symbolic computation, we show that this method is a valuable and efficient mathematical tool for solving application problems modeled by nonlinear partial differential equations (NPDE).