New exact traveling wave solutions of the coupled Boussinesq equations

This is the authors' abstract. We don't add key points for this paper.

• The coupled Boussinesq equation is studied. • New exact traveling wave solutions are obtained by the complete discriminant system within a polynomial approach. • The solutions are articulated through soliton, trigonometric, rational, and Jacobi elliptic functions. • Display 3D and contour plots and perform physical analysis. The Boussinesq equations, pivotal in the analysis of water wave dynamics, effectively model weakly nonlinear and long wave approximations. This study utilizes the complete discriminant system within a polynomial approach to derive exact traveling wave solutions for the coupled Boussinesq equation. The solutions are articulated through soliton, trigonometric, rational, and Jacobi elliptic functions. Notably, the introduction of Jacobi elliptic function solutions for this model marks a pioneering advancement. Contour plots of the solutions obtained by assigning values to various parameters are generated and subsequently analyzed. The methodology proposed in this study offers a systematic means to tackle nonlinear partial differential equations in mathematical physics, thereby enhancing comprehension of the physical attributes and dynamics of water waves.