Exact solutions of the Bogoyavlenskii equation using the multiple (G′G)-expansion method

In this work, exact traveling wave solutions of the Bogoyavlenskii equation are studied by the (G′G)-expansion method and its variants. The solutions obtained are general solutions which are in the form of hyperbolic, trigonometric and rational functions and a variety of special solutions like kink shaped, antikink shaped, bell type soliton solutions etc., can easily be derived from the general results under certain domain. These methods are more effective and simple than other methods and a number of solutions can be obtained at the same time. In order to visualize the underlying dynamics of the obtained solutions, two and three dimensional plots are drawn.