The Classification of the Single Traveling Wave Solutions to the Modified Fornberg–Whitham Equation

Abstract

The aim of present paper is to obtain the analytical solution of modified Fornberg–Whitham equation by using \(\tan (\phi /2)\)-expansion and \(\tanh (\phi /2)\)-expansion methods. These methods are used to construct solitary and soliton solutions of nonlinear evolution equation. These methods are straightforward and concise, and their applications are promising. These methods are developed for searching exact traveling wave solutions of nonlinear partial differential equations. The exact particular solutions containing five types hyperbolic function solution, trigonometric function solution, exponential solution, logarithmic solution and rational solution. The expansion methods presents a wider applicability for handling nonlinear wave equations. Also, their are shown that the expansion methods, with the help of symbolic computation, provide a straightforward and powerful mathematical tool for solving nonlinear evolution equations.