In this article, we will establish new impressive vision for the solitary solutions of Bogoyavlenskii-equation (BE) that represent the (2 + 1)-dimensional interaction of a Riemann wave propagation along definite axis along wave on the normal to it. A comparison between the achieved results from the point of view of three different mathematical analysis tool methods according to its personal profile name have been constructed. The three methods that included for this target are the Paul-Painlevé approach method (PPAM), the Ricatti-Bernoulli Sub-ODE method (RBSODM) and the third one is the variational iteration method (VIM).
The three suggested methods have been implemented at the same time and parallel to detecting different new visions for the solitary wave solutions of proposed model.