Research On The Influence Of High-order Effects On Peregrine Rogue Wave Comb And Transmission Dynamics In Non-uniform Fiber

Rogue waves,as a peculiar natural phenomenon in the ocean,have been a hots pot of research in recent years.In optical fibers,the nonlinear Schrodinger equation is a theoretical model for studying Peregrine rogue wave dynamics.Due to the material and characteristics of the fiber itself,including the variable coefficients into the nonlinear Schrodinger equation is an effective method to reflect the non-uniform effects of nonlinear pulses.Secondly,when the pulse width reaches the femtosecond level,high-order effects such as third-order dispersion,self-steeping,and self-frequency shift must be considered.Therefore,the high-order nonlinear Schrodinger equation with variable coefficients has become a classic model for studying Peregrine rogue wave dynamics.This thesis mainly introduces the research background of rogue waves and the progress in theory and experiment,the method of solving nonlinear Schrodinger equation and the types of exact solutions,including breathing solution and Peregrine rogue wave solution.On this basis,the compression points,the generation of Peregrine rogue wave combs and the transmission characteristics of pulse trains are studied.First,based on the breathing solution and the rogue wave solution of the variable coefficient high-order nonlinear Schr?dinger equation under the Hirota condition,the evolution characteristics of the breathing solution and the generation of the Peregrine rogue wave comb are studied.When the second-order dispersion and nonlinear effects take the form of periodic modulation,increasing the modulation intensity of the second-order dispersion coefficient will affect the spatial distribution of the rogue wave solution and form a comb-like structure in the transmission direction.And the number of compression points increases with the increase of the second-order dispersion modulation intensity,and the spatial frequency only affects the interval of the compression points.In addition,the introduction of a specific form of third-order dispersion will not affect the generation of the Peregrine rogue wave comb,and by modulating the coefficient of the third-order dispersion,the appearance of the secondary peak in the generation of the Peregrine rogue wave comb can be suppressed.Finally,we numerically simulated the high-order nonlinear Schrodinger equation with variable coefficients,compared the numerical solution with the exact solution,and provided a more flexible control method and related theoretical guidance for the nonlinear wave.Secondly,based on the exact solution of the variable coefficient Hirota equation,when the second-order dispersion takes the exponential form,the generation and transmission characteristics of the pulse train are studied in a fiber system with gradual dispersion.The results show that the amplitude of the dispersion coefficient and the attenuation coefficient affect the position of the stable pulse train.The third-order dispersion affects the initial velocity and deviation direction of the pulse train.Finally,in the presence of gain loss,the amplitude change of the pulse train during the propagation process is studied.The results of this paper enrich the theoretical research on the exact solution of the variable coefficient high-order nonlinear Schrodinger equation,and provide theoretical guidance for the practical application of optical communications.