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

Abstract In the paper, we take the (3+1)-dimensional KP-Boussinesq-like equation as an instance and utilize long wave limit approach to generate rational solution and semi-rational solution from the N-order soliton solution. For N = 2, 3, with specific parametric constraints, we have constructed rational solutions which can be presented as first order line rogue wave and single breather from two-soliton solution, and semi-rational solution is classified as first order kink-shaped rogue wave and a hybrid of breather and one soliton from three-soliton solution. For N = 4, the rational solution includes second order line rogue wave, double breather, interaction between two breathers and a hybrid of breather and line rogue wave. The semi-rational solution contains second order kink-shaped rogue wave and interaction between breather, soliton and line rogue wave. In addition, we give mathematical expressions for higher N-order rational solution.