Single-traveling-wave and double-wave polynomial solutions of the generalized (3 + 1)-dimensional modified Kadomtsev–Petviashvili equations with variable coefficients

Abstract

In this paper, we explore the generalized (3 + 1)-dimensional modified Kadomtsev–Petviashvili equations with variable coefficients, which are usually used in the fields of ferromagnetism, magneto-optics, plasma physics and fluid mechanics. For the sake of uncovering more physical phenomena related to this system, we consider the single-traveling-wave polynomial solutions in the light of the unified method and the double-wave polynomial solutions in line with the generalized unified method. Remarkably, the solitary-, soliton- as well as elliptic-type solutions are all discussed in these two kinds of solutions. Furthermore, the physical explanations of the solutions are given graphically and analytically for different choices of the free parameters (especially of the nonlinear coefficients of the equations that related to the physical insights). By discussing the wave propagation of each solution that we procured from the perspectives of amplitude, shape, symmetry or periodicity, we are capable of realizing the inherent characteristics of this equation commendably and discovering the correlative physical world more efficiently.