The Semirational Solutions Of The Maccari System:Degenerations And Resonances

The Maccari system is an important model for the description of two-dimensional nonlinear waves occuring in fluid dynamics and optics,etc.In this work,the semirational solutions and resonance of the Maccari system are investgated by employing the Hirota's bilinear method and reduction method of the KP hierarchy.A class of generalized semi-rational solutions of Maccari system are obtained,including dark soliton solutions,rational solutions and their mixed solutions.Firstly,we discuss the dark soliton solutions and rational so lutions which are the two degenerate forms of semi-rational solutions of Maccari system,as well as study their dynamical behavior respectively.Then,the elastic collision and resonance phenomena of general form the semi-rational solutions consist of dark soliton solutions and rational solutions are analysised.Finally,due to the resonant collisions,the line rogue waves and lumps in these semi-rational solutions become doubly localized in two-dimensional space and in time on a background of dark soliton solitons.The main results are as follows:1.With regard to the content,we have obtained a class of generalized semi-rational solutions of Maccari system.This is a novel family of solutions.2.The above mentioned semi-rational solution can provide two kinds rational solutions:lump and line rogue wave.3.About of dynamical behaviour analysis,the elastic collision and one kind of special unelastic collision(i.e.,resonance phenomena)are discussed.Taking different values of parameters in the semirational type solutions,we find the phenomena of partial resonance and completely resonance between dark soliton solutions and rational solutions.There exists fission and annihilation in partial resonance.However,two kinds of doubly localized rogue wave occur in completely resonance,which are doubly localized lump(rogue-type lump)and line segment rogue wave.