Abstract
Swarming with the waves, the oceans are never calm. Concerning certain dispersive long gravity waves on the shallow water of an open ocean, we check into a (2+1)-dimensional generalized dispersive long-wave system. In relation to the wave height above the undisturbed water surface as well as the horizontal velocity, we symbolically compute out two assemblies of the hetero-Bäcklund transformations and two assemblies of the similarity reductions. Each assembly either brings about a known (2+1)-dimensional Broer-Kaup-Kupershmidt system or comes to a known ordinary differential equation. Also, each assembly relies on the coefficients from the original system.
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