Diversity of interaction phenomenon, cross-kink wave, and the bright-dark solitons for the (3 + 1)-dimensional Kadomtsev–Petviashvili–Boussinesq-like equation

Abstract

The (3 + 1)-dimensional Kadomtsev–Petviashvili–Boussinesq-like equation has certain advantages in solving engineering problems. In this paper, based on the generalized bilinear form, we successfully derived the diversity of exact solutions under certain constraints by using the symbolic computation Maple. These solutions have interaction wave solitons, cross-kink wave solitons, and bright-dark solitons. To ensure the accuracy of these solutions, we made a special selection of the parameters involved and made a three-dimensional graph, density graph, and contour graph to illustrate the dynamics of the solutions. The resulting solutions can be used for the study of certain phenomena in physics.

Rational and semi-rational solution to the (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq-like equation

“…For equation (1), Yu et al have constructed a direct bilinear Bäcklund transformation [34]; Lu et al got diversity of interaction solutions by bilinear form [35]; Manafian obtained multiple rogue wave solutions for this equation and the linear superposition principle [36]; Liu et al researched the interaction phenomenon between lump solitons [37]; Han et al have described the three-wave solutions and periodic wave [38].…”