Abundant wave solutions of the Boussinesq equation and the (2+1)-dimensional extended shallow water wave equation

Abstract

In this article, we establish the exact wave solutions of the Boussinesq equation and the (2 + 1)-dimensional extended shallow water wave equation by applying the new generalized (G'/G) -expansion method. When the condition of the fluid is such that the horizontal length scale is much greater than the vertical length scale, the shallow water equations are mostly suitable. In Ocean engineering, Boussinesq-type equations are commonly used in computer simulations for the model of water waves in shallow seas and harbors. We explained the new generalized (G'/G) -expansion method to seek further general traveling wave solutions of the above mentioned equations. The traveling wave solutions attained by this method are exposed in terms of hyperbolic, trigonometric and rational functions. The shape of the obtained solutions are bell shaped soliton, kink soliton, singular kink soliton, singular soliton, singular periodic solution and compaction. This method is very influential mathematical tool for extracting exact solutions of NLEEs which frequently arise in mathematical physics, engineering sciences and many scientific real world application fields.