Explicit Solutions for the Nonlinear Pochhammer-Chree Equation Utilizing Enhanced Tanh-Function Expansion Scheme and a Direct Approach

Abstract

In this paper, we will apply the tanh-function scheme with the aid of Maple software to construct   new explicit wave solutions of the nonlinear Pochhammer-Chree equation. Also, we use a direct algebraic method based on the Liénard equation to find other diffrent new explicit solutions. Soliton solutions, periodic solutions and rational functions solutions are obtained. Comparing our new results obtained in this paper with the well-known results are given. Further, some 2D and 3D graphs of the obtained explicit traveling wave solutions are shown. Finally, the tanh-function expansion scheme presented in this paper is straightforward, concise and it can also be applied to other nonlinear partial differential equations in mathematical physics.