Theoretical Study On Rogue Wave And Breather On Localized And Periodic Backgrounds With Time-Space Modulation

The dynamics of localized waves on the plane-wave background has become a hot topic in many nonlinear physical systems.However,the infinite-wide plane-wave background does not exist in real physics,the localized waves solution on the plane-wave background can not adequately describe the real nonlinear physical phenomena.On the other hand,a plane wave,upon which these solutions are built,is simply a limiting cases of the periodic waves.From a statistical perspective,these periodic oscillations appear common in the ocean.In fact,in the experiment of water tank,the rogue waves are excited on a regular wave train(periodic wave).It is also common for an optical periodic wave to appear in a fiber as a regular train of solitonic pulses.In practical nonlinear physical systems,localized and periodic backgrounds are two common types of easy-to-prepare backgrounds.Therefore,it is very important to study the excitation and evolution of localized waves on localized and periodic background.In this paper,we study several properties of the nonlinear localized waves excitation and laws of the nonlinear evolution theoretically on localized and periodic backgrounds,which in-cludes the general breather,Kuznetsov-Ma breather,Akhmediev breather and Peregrine rogue wave.We present the general analytical solutions for the generalized nonlinear Schrodinger equation with time-space modulation via the method of a combination of the Darboux trans-formation and similarity transformation.According to the analytical solution,we first confirm the existence of localized waves on localized and periodic backgrounds.Then we analyze the influence of the localized background height and width on the localized wave excitation and evolution properties.We find that the wider the width of the localized background,the smaller the background amplitude.The amplitude of the localized wave decreases as the amplitude of localized background decreases until it disappears.On the other hand,we study the amplitude of periodic background and frequency effects on localized wave excitation and evolution prop-erties.We find that with the change of the periodic background amplitude,there exists highly different peaks in localized wave.The change of frequency affects the distribution of the highly different peaks.In particular,we analyze the effect of manipulable parameters on the localized wave properties in nonlinear optical systems and Bose-Einstein Condensates.The results will provide a theoretical reference for the understanding of the physical properties,whose excita-tion and evolution are in local and periodic backgrounds,and experimental excitation.