On a (3 + 1)-dimensional generalized variable-coefficient Camassa-Holm-Kadomtsev-Petviashvili equation in ocean physics, hydraulic engineering and modern physics

Evidences from Int. J. Mod. Phys. B have indicated that the contemporary investigations into ocean physics, hydraulic engineering and modern physics remain highly dynamic and vigorous. In ocean physics, hydraulic engineering and modern physics (e.g., for the shallow water waves), a (3+1)-dimensional generalized Camassa-Holm-Kadomtsev-Petviashvili equation has recently attracted people’s attention. The present study explores a variable-coefficient extension of that equation via symbolic computation and works out an auto-Bäcklund transformation via a non-characteristic movable singular manifold, along with four families of the solitonic solutions and two families of the rational solutions. All the results in this paper, concerning the wave amplitude, are dependent on the variable coefficients in that extension, while those coefficients respectively lead the nonlinearity, dispersion and transverse variations of the wave in the three directions, employed to suggest the function of dispersion in the emergence of patterns. Imposed variable-coefficient constraints are given. Various choices of those coefficients might prove helpful for investigating the underlying mechanisms via our auto-Bäcklund transformation, solitonic and rational solutions, for that extension in ocean physics, hydraulic engineering and modern physics. Our findings might contribute to the theoretical ground work for future inquiries in ocean physics, hydraulic engineering and modern physics.