Considering the Shallow Water of a Wide Channel or an Open Sea Through a Generalized (2+1)-dimensional Dispersive Long-wave System

Under investigation in this paper is a generalized (2+1)-dimensional dispersive long-wave system, describing the nonlinear and dispersive long gravity waves in two horizontal directions in the shallow water of a wide channel of finite depth or an open sea. Via symbolic computation, we derive the same bilinear forms as those reported, but through a different method. Four sets of the similarity reductions are obtained, each of which leads to a known ordinary differential equation. The results rely on the coefficients in the original system, with respect to the horizontal velocity and wave elevation above the undisturbed water surface.