New interaction of high-order breather, periodic-wave, lump, rational soliton solutions and mixed solutions for the Hirota–Maccari system

Abstract

The higher-order breather, periodic-wave, lump, rational soliton solutions and mixed solutions of the Hirota–Maccari (HM) system by virtue of the Kadomtsev–Petviashvili (KP) hierarchy reduction method are investigated in this work. Through analyzing the structural characteristics of periodic-wave solutions, we attain the quasi-periodic W(M)-shaped waves and two kinds of breathers. The mixed solutions that consist of the quasi-periodic W(M)-shaped waves and breathers are constructed. Further, by taking the long wave limit on the periodic-wave solutions, the semi-rational solutions are derived, which illustrate the interaction of the rational soliton, lump, quasi-periodic wave and breather. Characteristics of these mixed solutions are discussed graphically and the corresponding generating conditions are given. Especially, a new bound-state interaction composed of lump and breather is generated under the velocity resonance mechanism. This newfangled pattern is a beautiful phenomenon for the HM system.