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In this paper, we have described two dreadfully important methods to solve nonlinear partial differential equations which are known as exp-function and the exp(− ϕ ( ξ )) -expansion method. Recently, there are several methods to use for finding analytical solutions of the nonlinear partial differential equations. The methods are diverse and useful for solving the nonlinear evolution equations. With the help of these methods, we are investigated the exact travelling wave solutions of the Vakhnenko- Parkes equation. The obtaining soliton solutions of this equation are described many physical phenomena for weakly nonlinear surface and internal waves in a rotating ocean. Further, three-dimensional plots of the solutions such as solitons, singular solitons, bell type solitary wave i.e. non-topological solitons solutions and periodic solutions are also given to visualize the dynamics of the equation.

Investigation of Solitary wave solutions for Vakhnenko-Parkes equation via exp-function and Exp(−ϕ(ξ))-expansion method