On Assorted Soliton Wave Solutions with the Higher-Order Fractional Boussinesq–Burgers System

The purpose of this study is to highlight the shallow water wave patterns along the ocean shore or in lakes with the higher-order Boussinesq–Burgers system possessing a fractional derivative operator. A generic fractional transformation is used, which turns the proposed model into an nonlinear ordinary differential equations (NLODEs) system. For the construction of new solitons of the mentioned coupled system, the auxiliary equation technique is employed. This approach produced numerous soliton solutions such as bright, singular and w-shaped solitons of the aforesaid model successfully. These results are expressed graphically to exemplify their physical appearance with the help of soft computations in Mathematica. All the solutions yielded by this method are novel and have not been derived yet.