Towering and internal rogue waves induced by two-layer interaction in non-uniform fluid. A 2D non-autonomous gCDGKSE

Abstract

AbstractA Generalized (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada equation (2D- gCDGKSE) is an integro-differential equation that describes tow-layer fluid interaction. The non-autonomous (2+1)-dimensional gCDGKSE (NAUT-gCDGKSE) was rarely considered in the literature. In the previous works, the concepts of two-layer fluid interaction and non-uniform fluid were not explored. This motivated us to focus the attention on these themes. Our objective is to inspecting waves structures in non-uniform fluid which describes fluid flows near a solid boundary. Thus, the present work is completely new. Our objective, here, is to inspect waves which are similar to those created in waterfall, water waves behind dams, boat sailing, in the network of canals during water release, and internal waves in submarine. In a uniform fluid, rogue waves occur in open oceans and seas, while in the present case of non-uniform fluid, towering and internal rogue waves occur near barriers (islands) and near submarine, respectively. This was consolidated experimentally, as it was shown that rogue wave is produced in a water tank (which is with solid boundary). The exact solutions of NAUT-gCDGKSE are derived here, by implementing the extended unified method (EUM). In applications, it is found that the EUM is of lower time cost in symbolic computation, than when using Lie symmetry, Darboux and AutoBucklund transformations. The results obtained here are evaluated numerically, and they are displayed in graphs. They reveal multiple waves structures with relevance to waves created near a solid boundary. Among them are towering and internal rogue waves, internal (hollowed) and bulge-U-shape wave and S-shape wave, water fall, saddle wave, and dromoions.