Exact solutions of extended shallow water wave equations by exp-function method

Purpose - The purpose of this paper is to apply the exp-function method to construct exact solutions of nonlinear wave equations. The proposed technique is tested on the (2 + 1) and (3 + 1) dimensional extended shallow water wave equations. These equations play a very important role in mathematical physics and engineering sciences. Design/methodology/approach - In this paper, the authors apply the exp-function method to construct exact solutions of nonlinear wave equations. Findings - In total, four forms of the extended shallow water wave equation have been studied, from the point of view of its exact solutions using computational method. Exp-function method was employed to achieve the goal set for this work. The applied method will be used in further works to establish more entirely new solutions for other kinds of nonlinear wave equations. Finally, it is worthwhile to mention that the proposed method is straightforward, concise, and it is a promising and powerful new method for other nonlinear wave equations in mathematical physics. Originality/value - The algorithm suggested in the paper is quite efficient and is practically well suited for use in these problems. The method is straightforward and concise, and its applications are promising.