The Excitation Of Localized Waves And Theirinteraction In Nonlinear Fiber System

Dynamics of nonlinear localized wave is one of the important branches of nonlinear science,which recently has become a hot topic.The study of nonlinear localized waves is pushed to a new level,especially the application of nonlinear local wave in the field of high channel rate optical soliton communication,laser mode-locking,ultrafast optics,generation of highenergy optical pulse,supercontinuum generation and frequency combs,etc.The basic localized waves include soliton,rogue wave and breather.Soliton propagates stably and possesses both wave and particle properties.Rogue wave is a special type of localized waves with high energy and short life and its peak is much higher than the background,which appears from nowhere and disappears without a trace.Breather is a localized wave with breathing characteristics in one direction and there is a periodic energy exchange between breather and the background.Scientists have done a lot of research in nonlinear field and gotten many significant results.However there are still some problems that are not thoroughly solved.Further research and discussion are necessary,for studying the physical generation mechanism of localized waves,the regulations of interaction between different localized waves,and the intrinsic relationship between different localized waves,etc.This paper is based on the theoretical and experimental results of predecessors and uses both analytical and numerical methods to explore a new model of soliton excitation,study the interaction between rogue wave and breather,reveal the state transition between rogue wave and solitons and analyze the mechanism of this transition.The details are as follows:Firstly,the interaction between the breather and the rogue wave is studied in a nonlinear single-mode fiber.The standard nonlinear Schr¨odinger equation is used to describe the system,and the exact solution of the system is constructed by Darboux transformation and other methods.The impacts of the relative phase and initial relative position offset are discussed in detail based on exact solution.It is shown that the aggregate structure of high-order rogue waves will be ”divided” by the breather in the cases of nonzero relative phase or nonzero relative position offset,which can be used to reduce the maximum hump value and change the temporal-spatial distribution of high-order rogue waves.We also qualitatively reveal the characteristic of exclusion between Kuznetsov-Ma breathers and high-order rogue waves,which is weakened when the initial relative position offset increases.Their interaction properties are characterized by the trajectory of localized waves' valleys and humps,which shows that the interaction of nonlinear localized waves changes the dynamical evolution trajectory of rogue waves and breathers radically.These results provide a new idea for effectively controlling rogue wave.Secondly,we study the influence of higher-order effects with different orders on localized wave dynamics.Due to the special modulation instability gain distribution of the optical system with fourth-order effect,we study the state transition between rogue wave and soliton in the system.The characteristics of state transition are analyzed when the rogue wave transition from the unstable region of the modulation to stable region.The result is quite different from the state transitions in other models.We find that the dynamics of different rogue waves on different regimes is distinct.A lot of interesting structures of nonlinear localized waves are obtained from the state transition.Considering the corresponding relation between modulation instability gain distribution and structure of nonlinear localized waves,a general rule can be found,which is that on two stable lines rogue waves transform to asymmetrical structure and the structure of nonlinear localized waves on left line is a mirrored version of nonlinear localized waves on right line.Along with the approach of two stable lines,the asymmetrical structure will change.When two stable lines cross with each other,rogue wave transforms to a symmetrical structure.Interestingly,the localized wave structures on the left and right stable lines are mirror symmetry,which is consistent with the mirror symmetry of modulation instability gain.It will deepen our knowledge of the relationship between modulation instability and nonlinear excitation.By using of trajectory of peaks and valleys,the rule of evolution is revealed.We discuss the excitation and state transition of multi-peak solitons in an optical system with fifth-order effect.We exhibit abundant nonlinear localized waves and the condition of their excitation.We emphatically study the rule of transition between symmetric and asymmetric multi-peak solitons,which is induced by initial phase,and demonstrate the transition condition exactly.It will greatly help to establish connections between symmetric and asymmetric solitons and deepen our knowledge of multi-peak solitons.Finally,we study the excitation of soliton on continuous waves background in an exponential dispersion decreasing fiber with two orthogonal polarization states.We demonstrate that asymmetric soliton pulse,which is a new mode of soliton excitation,can be generated from a weak modulation on continuous waves background.We provide one theoretical method to effectively control the symmetric degree of the asymmetric soliton pulse by changing the relative frequency of the two components.In addition,we find that there is an “asymmetric discontinuous spectrum”in the frequency spectrum of asymmetric soliton.It greatly enriches the structure of soliton and provides a theoretical reference for experimentally obtaining asymmetric solitons.