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

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.

Automated summary

In this work, the higher-order breather, periodic-wave, lump, rational soliton solutions, and mixed solutions of the Hirota-Maccari (HM) system are investigated. The Kadomtsev-Petviashvili (KP) hierarchy reduction method is employed to analyze the structural characteristics of these solutions. The study reveals the quasi-periodic W(M)-shaped waves and two types of breathers in the periodic-wave solutions. Mixed solutions, consisting of the quasi-periodic W(M)-shaped waves and breathers, are constructed. The characteristics and generating conditions of these mixed solutions are discussed, and a new bound-state interaction composed of a lump and a breather is discovered.