New families of soliton solutions for two nonlinear (2+1)- and (3+1)-dimensional generalized Camassa–Holm–Kadomtsev–Petviashvili (g-CHKP) equations in modern physics

In this paper, we investigated the extraordinarily complex nonlinear evolution equations [Formula: see text]- and [Formula: see text]-dimensional generalized Camassa–Holm–Kadomtsev–Petviashvili (g-CHKP) equations found in shallow water waves. We use the Jacobi Elliptic Function Expansion (JEFE) method to derive a variety of closed-form analytical soliton solutions, and traveling wave solutions for the nonlinear [Formula: see text]- and [Formula: see text]-dimensional generalized g-CHKP equations. Several new forms of soliton-like solutions to the governing equations, as well as the dynamics of various types of solutions, are shown graphically for selecting the relevant parameters via numerical simulation. The originality of this work arises from the fact that the results mentioned are entirely new and have not before been studied for the given equation. Furthermore, the applied mathematical approach is more efficient and trustworthy for developing newly constructed soliton solutions in various fields of complex nonlinear phenomena. We anticipate that the findings of this work will have important applications in plasma physics, ocean engineering, optical fibers, quantum mechanics, fluid dynamics, nonlinear dynamics, and soliton theory.