Generalized (G’ / G) – expansion method for the loaded shallow water wave equation

Abstract

This article is devoted to finding solutions for the traveling wave of the loaded wave equation in shallow water. One of the approaches to finding solutions by the expansion method (G / G) is given, which is one of the most effective ways to obtain solutions. When parameters are taken as special values, solitary waves are also derived from traveling waves. Solutions for the traveling wave are expressed by hyperbolic and trigonometric functions. This method is easy to implement using well-known software packages that allow solving complex nonlinear evolutionary equations of mathematical physics.