Rational and semi-rational solutions of the Kadomtsev–Petviashvili-based system

Abstract

We investigate the rational and semi-rational solutions of the integrable Kadomtsev–Petviashvili (KP)-based system, which appears in fluid mechanics, plasma physics, and gas dynamics. Various types of solutions, including soliton, breather, and a mixture of breather and soliton, of the KP-based system are derived by applying the Hirota’s bilinear method and the perturbation expansion. By taking a long-wave limit of the soliton solutions and particular parameter constraints, the rational and semi-rational solutions are generated. The rational solutions have two different dynamical behaviors: lump and line rogue wave; the first-order lump and line rogue wave are classified into three patterns: bright state, mixed state, and dark state. The semi-rational solutions reveal the following dynamic features: (1) Elastic interactions between lumps and bound-state dark solitons; (2) Elastic interactions between line rogue waves and bound-state dark solitons; (3) Inelastic collisions of breathers and rogue waves. Compared to the rational solutions, the semi-rational solutions have more interesting patterns.