Author(s)

Luwai Wazzan

Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia.

The modified tanh-coth function method is used to obtain new exact travelling wave solutions for Zhiber-Shabat equation and the related equations: Liouville equation, sinh-Gordon equation, Dodd-Bullough-Mikhailov equation, and Tzitzeica-Dodd-Bullough equation. Exact travelling wave solutions for each equation are derived and expressed in terms of hyperbolic functions, trigonometric functions and rational functions. The modified tanh-coth function method is easy to execute, brief, efficient, and can be used to solve many other nonlinear evolution equations.

A Modified tanh-coth Function Method, Zhiber-Shabat Equation, Liouville Equation, sinh-Gordon Equation, Dodd-Bullough-Mikhailov Equation, Tzitzeica-Dodd-Bullough Equation, Travelling Wave Solutions, Solitary Wave Solutions

Wazzan, L. (2016) Solutions of Zhiber-Shabat and Related Equations Using a Modified tanh-coth Function Method. Journal of Applied Mathematics and Physics, 4, 1068-1079. doi: 10.4236/jamp.2016.46111.