State Transition Of Breather And The Characteristics Of Nonlinear Stage Of Modulation Instability

In this paper,based on the existing physical models,we solve nonlinear equations by Darboux transformation method and use corresponding mathematical software for numerical simulation.We mainly study the state transition between the breathers and the solitons,and the characteristics of the modulation instability nonlinear stage.The details are as follows:(1)The state transition between localized waves of a variable-coefficient NLS equation with higher-order effectsFirstly,we introduce the state transition between the breathers and the solitons caused by the higher-order effects,and give an analytical expression for the transition condition.Secondly,we mainly study the influence of higher-order effects and nonautonomous effects on the multi-peak solitons.We find that higher-order effects affect the velocity,localization and compression effects of the multi-peak solitons,while autonomous effects affect the number of peaks of the multi-peak solitons.Finally,we analyse the relation between the state transition and modulation instability,namely,state transition condition is consistent with the modulation stability region condition when the rogue wave eigenvalue is taken.These results are helpful to the experimental design and manipulation of the optical rouge wave.(2)Superregular breathers(SRBs)and state transition of a Nonlinear Schrodingerand the Maxwell-Bloch(NLS-MB)equationwe first study the SRBs solution in the coupled NLS-MB system and realize the state transition of SRBs and solitons.Then,we discuss the characteristics of the modulation instability nonlinear stage,it can be made by three models:a SRB and a multi-peak soliton,two multi-peak soliton,a multi-peak soliton and a W-shaped soliton,which are developed from a small localized perturbation.Finally,we analyse the relation between the state transition and the linear modulation instability.Our results enrich the form of state transition in nonlinear physical models.