Resonance Soliton, Breather and Interaction Solutions of the Modified Kadomtsev–Petviashvili-II Equation

Abstract

In this paper, we investigate the modified Kadomtsev–Petviashvili-II (mKP-II) equation, which has important applications in fluid dynamics, plasma physics and electrodynamics. By utilizing the Hirota bilinear method, the N-soliton solutions of the mKP-II equation are obtained. The resonance Y-type soliton, and the interaction between M-resonance Y-type solitons and P-resonance Y-type solitons are constructed by imposing some constraints to the parameters of the N-soliton solutions. Moreover, the novel type of double opening resonance Y-type soliton solutions are obtained by selecting some appropriate parameters in 3-soliton solutions. By making some conjugate assumptions in the parameters, the multiple breathers are presented. Furthermore, the hybrid solutions consisting of multiple breathers and resonance Y-type solitons are investigated. The dynamics of these hybrid solutions are analyzed using both numerical simulations and graphical methods.