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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.

international journal of nonlinear sciences and numerical simulation

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