The -expansion method is used to obtain new exact travelling wave solutions for the Zhiber-Shabat equation and the related equations: Liouville equation, sinh-Gordon equation, Dodd-Bullough-Mikhailov equation, and Tzitzeica-Dodd-Bullough equation. Travelling wave solutions of these different physical structures are formally derived for each equation and expressed in terms of hyperbolic functions, trigonometric functions and rational functions. The proposed method is direct, concise, elementary and effective, and can be used for many other nonlinear evolution equations.

-expansion method, Zhiber-Shabat equation, Liouville equation, Sinh-Gordon equation, Dodd-Bullough-Mikhailov equation, Tzitzeica-Dodd-Bullough equation, travelling wave solutions, solitary wave solution.