This work considers the Liouville equation, the sinh-Gordon equation and special form of Zhiber-Shabat equation, arising in mathematical biology. The extended sine-cosine method has been used in order to obtain multiple exact special solutions. The proposed scheme can be applied to a wider class of nonlinear equations.

extended sine-cosine method, Zhiber-Shabat equation, Liouville equation, sinh-Gordon equation, solitons solutions, travelling wave solutions, exponential solutions.