Study On Rogue Wave And Nonlinear Composite Waves In Nonautonomous Fiber Systems

Optical rogue waves(RWs),as own high-amplitude and broad spectrum,have important application propects in optical research such as the generation of high-power pulses and supercontinuum.An important research branch of optical RWs is to seek exact solutions in various theoretical models.The research of exact solutions is helpful to understand the generation mechanism of RWs and discover new characteristics of RWs in different optical systems.Moverover,it can provide theoretical basis for the generation and control of RWs in optical experiments.At present,the theoretical models for studing optical RWs have been extended from basic model to the higher-order models,from single mode fiber system to coupled system,and the exact solutions have been developed from fundamental RW solution to higher-order RW solutions or semirational RW solutions.Moreover,the study of the composite waves superposed by nonlinear waves such as Peregrine RW and breathers in coupled nonautonomous systems is helpful to understand the generation mechanism of the higher-order RWs and discover the interesting features of diverse nonlinear composite waves.In this thesis,considering variable coefficient(coupled)nonautonomous nonlinear Schr?dinger(NLS)equation and adopting similarity transformation,we study the controllable excitation of higher-order RWs,the generation of high-power pulse(train),the interactions of nonlinear waves and the diversity of composite waves,which are related to RWs,in inhomogeneous nonautonomous fiber systems.The presented results can provide theoretical guidance for the generation of controllable higher-order RWs in optical experiments and the controllability of composite waves.The contents of this thesis are as follows:(1)Based on the variable coefficient nonautonomous NLS equation,a semirational RW solution describing the nonlinear superposition of Peregrine RW and breathers is derived.With the aid of the analytical solution,we study the interactions between Peregrine RW and Akhmediev breather(AB)or Kuznetsov-Ma breather(KMB),and the controllability of the semirational RW in periodic distribution and exponential decreasing nonautonomous systems with linear and harmonic potentials.The results show that the harmonic potential affects the existence condition of the semirational RWs and the linear potential influences the semirational RW's trajectory,while the dispersion and nonlinearity parameters determine the position and the degree of the excitation of the higher-order RWs.The higher-order RWs merged in the breathers can be partly,completely or biperiodically excited in periodic distribution nonautonomous system,while there are diverse excitation patterns in exponential decreasing nonautonomous system by changing the dispersion and nonlinearity parameters.These results reveal that the higher-order RW excitation can be controlled in the inhomogeneous nonautonomous system by choosing dispersion,nonlinearity and external potential parameters.(2)A simple scheme for generating high-power pulse,pulse pairs,and pulse trains in a dispersion decreasing nonautonomous fiber system is proposed.Acoording to the scheme,pulse train with invariable amplitudes can be generated from the first-order AB,and the high power pulse and pulse pair can be generated from the second-order KMB in dispersion decreasing fiber by selecting appropriate fibre parameters.It is found that the period of the pulse trains is only related to the eigenvalue parameter,while the power and the full width of half-maximun of the pulses,and the interval of the pulse pairs can be controlled by adjusting the eigenvalue parameter and fiber parameters,and the pulse velocity at the initial stage is affected by linear potential.(3)Based on the variable coefficient coherently coupled nonautonomous NLS model,a composite wave solution describing the superposion of soliton and AB,KMB or Peregrine RW is presented.With the aid of the obtained solution,the interactions between soliton and AB,KMB or Peregrine RW are studied in exponentially decreasing and periodic perturbation nonautonomous systems.The results show that there exist three types of collisions including elastic collision,quasi-elastic collision and inelastic collision between the soliton and the AB while there is only elastic collision between the soliton and the KMB or the Peregrine RW.Moveover,the amplitude variation of the composite wave with the propagation distance can be changed by controlling the relationship between the decay rates of the dispersion and nonlinearity parameters;both the dispersion and nonlinearity perturbation can result in the amplitude fluctuation of the soliton and background of the composite waves,but only the dispersion perturbation leads to the fluctuation of the soliton trajectory while the nonlinearity perturbation can not affect the soliton trajectory.(4)Based on the variable coefficient coherently coupled nonautonomous NLS equations with harmonic external potentials,we derive three types of similarity transformations which can transform the variable coefficient coupled nonautonomous NLS equations into constant coefficient coupled NLS equations,and the latter can be further decoupled to two independent NLS equations by a linear transformation.With the help of the various solutions of NLS equation and the deduced three similarity transformations,we investigate the diverse dynamic of six composite waves superposed by different nonlinear waves in nonautonomous systems.The results show that the periodic energy exchange between two coupled components can be suppressed by choosing appropriate parameters.Taking the composite wave superposed by soliton and AB as an example,we study the diverse evolution of the composite waves in the tunneling system and periodic perturbation system under three types of similarity transformations.It is found that in the tunneling system,the amplitude,velocity and period of the AB and the collision position of the two nonlinear waves exhibit different characteristics for different similarity transformations;in the periodic perturbation system,the width and trajectory of the composite waves are affected by the nonlinearity perturbation when adopting similarity transformation I,while by the dispersion pertubation when adopting similarity transformation II,but neither by dispersion pertubation nor by nonlinear perturbation when adopting similarity transformation III.