Multiple rogue wave solutions of the (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation

Abstract

Based on a symbolic computation approach and the Hirota’s bilinear method, the multiple rogue wave solutions of the (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation, which can be regarded as a generalization of the generalized rational solutions of Boussinesq equation proposed by Clarkson and Dowie, are constructed. The first-order, second-order, third-order and fourth-order rogue waves are systematically discussed. Moreover, the maximal amplitude and the minimum amplitude of the first-order rogue wave solutions are given. By choosing some specific parameters of these rogue wave solutions, their dynamic behaviors are analyzed.