Periodic line wave, rogue waves and the interaction solutions of the (2+1)-dimensional integrable Kadomtsev–Petviashvili-based system

This paper mainly investigates multiple types of solutions for the (2+1)-dimensional integrable Kadomtsev–Petviashvili-based system, which can describe the complex nonlinear wave phenomena observed in many physical systems, such as fluid mechanics, plasma physics and ocean dynamics. The Hirota’s bilinear method and the perturbation expansion skill are used to derive the periodic line wave solution and the interaction solution composed of the breather and the periodic line wave. By choosing appropriate parameters and employing the long wave limit of the soliton solution, two kinds of elementary rogue waves (RWs) are generated, which are kink-shaped line RW and W-shaped line RW. The interaction solutions among a lump, two lumps and two kinds of line RWs are obtained. Furthermore, the semi-rational solutions of the KP-based system are yielded, which include six types, namely (1) a line RW on a line soliton background, (2) a line RW on two line solitons background, (3) the line RW on the breather background, (4) a lump on the background with the periodic line wave, (5) the line RW on the background of the lump and the breather and (6) two lumps on the background with the periodic line wave. An effective analytical method related to the characteristic lines is presented to analyze the dynamical behaviors of the rogue waves and interaction waves. The method can be further extended to investigate other complex wave structures for the high-dimensional nonlinear integrable equations.