Traveling wave solution of (3+1)-dimensional negative-order KdV-Calogero-Bogoyavlenskii-Schiff equation

We explored the (3+1) -dimensional negative -order Korteweg-de Vries-alogeroBogoyavlenskii-Schiff (KdV-CBS) equation, which develops the classical Korteweg-de Vries (KdV) equation and extends the contents of nonlinear partial differential equations. A traveling wave transformation is employed to transform the partial differential equation into a system of ordinary differential equations linked with a cubic polynomial. Utilizing the complete discriminant system for polynomial method, the roots of the cubic polynomial were classified. Through this approach, a series of exact solutions for the KdV-CBS equation were derived, encompassing rational function solutions, Jacobi elliptic function solutions, hyperbolic function solutions, and trigonometric function solutions. These solutions not only simplified and expedited the process of solving the equation but also provide concrete and insightful expressions for phenomena such as optical solitons. Presenting these obtained solutions through 3D, 2D, and contour plots offers researchers a deeper understanding of the properties of the model and allows them to better grasp the physical characteristics associated with the studied model. This research not only provides a new perspective for the in-depth exploration of theoretical aspects but also offers valuable guidance for the practical application and advancement of related technologies.