Modulation Instability Analysis And Nonlinear Wave Excitation Modes In Nonlinear Schr(?)dinger-typed Equations

The calculation of nonlinear waves and modulation instability(MI)analysis are one of the hot topics in soliton dynamics research.In this paper,based on several types of nonlinear Schr(?)dinger-typed(NLS)equations,by using Darboux transformation and linear stability analysis,we study the corresponding relations between the various nonlinear waves under nonzero background and MI,the interaction mechanism between different waves and the superregular breathers dynamics.The details are as follows:1.The relations between the nonlinear wave excitation modes under nonzero background and MI for the fifth-order NLS equationFirstly,we study the linear stability analysis of this equation,and obtain the different types of nonlinear waves solutions by using Darboux transformation,further present the corresponding relations and phase diagram between these waves and MI.Secondly,by introducing the perturbation energy to locate the solitons,and we show that solitons in the MI regime are caused by both the fourth-and fifth-order effects.Finally,we perform numerical simulation to test the stability of the antidark soliton.2.The nonlinear wave excitation modes under nonzero background and MI in an erbium-doped fiberWe study the nonlinear wave dynamics and MI under a constant background for the coupled nonlinear Schr(?)dinger and the Maxwell-Bloch equations,and display the characteristics of interactions between the nonlinear waves,mainly including elastic collision,semi-elastic collision and inelastic collision.3.The dynamics of the superregular breathers for a fourth-order generalized NLS equation with variable coefficientWe study the first-order quasi-Akhmediev breather,the second-and third-order superregular breather solutions for a fourth-order generalized NLS equation with variable coefficient.According to the relation between the group velocity and phase velocity,we analyze the dynamics of superregular modes,mainly including the standard,half-transition and full-transition superregular modes.Finally,we analyze the dynamics characteristics of the superregular modes by changing the fourth-order dispersion coefficient(based on the periodical dispersion and exponential dispersion management).