Exact solutions of a fifth - order Korteweg–de Vries –type equation modeling nonlinear long waves in several natural phenomena

Abstract

In this study we discuss existence of solitary wave solutions of a famous higher-order model evolution equation arising from the water wave theory. This evolution equation describes several nonlinear natural phenomena such as propagation of long waves in shallow water over a flat surface or propagation of long gravity-capillary waves. We obtain several exact analytical solutions of this equation by applying a particular case of the Simplest Equations Method (SEsM).Numerical simulations of the obtained solutions include various kinds of solitary waves depending on a key model parameter.