Exploring traveling wave solutions and conservation laws of the Whitham–Broer–Kaup dynamical model with stability and applications

In this paper, we present novel exact traveling wave solutions for the coupled Whitham–Broer–Kaup equation, which includes both odd- and even-order partial derivative terms. These solutions are obtained using the extended generalized Riccati equation mapping method. The resulting traveling wave solutions exhibit diverse forms, including bright solitons, periodic waves, breather solitons, lump solitons, and others. Furthermore, the stability and conservation laws associated with these solutions are analyzed in detail. These findings have significant implications in physics and various applied sciences. In addition, the proposed method proves effective for solving a broader class of coupled nonlinear partial differential equations.