Study On Localized Wave Solutions Of Three Types Multi-component Coupled Nonlinear Equations In Nonlinear Optical Fibers

With the deepening of research,considering the complexity and diversity of nonlinear systems,multi-component coupled nonlinear equations have gradually become a hot spot in the field of nonlinear science,and their localized wave solutions have richer dynamic characteristics than single-component systems,which can provide more theoretical basis for the application of localized waves in practical engineering.This paper is based on three multi-component coupled nonlinear systems in nonlinear optical fibers,using the Darboux transformation and the generalized Darboux transformation,the expression of the localiaed wave solution of the equation is derived,and the corresponding evolution diagram is obtained through numerical simulation.In addition,the dynamic properties of the localized wave solution are studied.The paper is divided into the following contents:The first chapter is the introduction of this article,introducing the research background and significance,local waves,and generalized Darboux transformation methods.In chapter 2,based on the two component coupled Gerdjikov-Ivanov equation and its Lax pair equation describing the propagation of optical solitons in nonlinear optical fibers,the iterative expression of higher-order solitons is obtained using the generalized Darboux transformation;According to the classification discussion on whether the real and imaginary parts of the spectral parameters are equal,the dynamic properties such as the propagation direction and energy magnitude of the higher-order soliton solution are analyzed.The results show that spectral parameters can change the signal transmission trajectory of optical solitons,and higher order optical solitons exhibit two dynamic properties: elastic collision and inelastic collision during the transmission process.In chapter 3,based on the three component coupled Hirota equation and the special solution of Lax to the equation that describes the transmission of optical pulses,the first order soliton solution expression of the equation is obtained by using the generalized Darboux transform and Darboux dressing transform.Taylor expansion is carried out on it and small parameters are introduced into the spectral parameters to further obtain the expression of rogue wave solution,adjust the parameters in the expression,and obtain different propagation forms of optical signals through numerical simulation.The results show that spectral parameters determine the propagation mode of optical signals and affect the local maximum variation of optical signals.Chapter 4 is based on describing the three component coupling nonlinearity Schr(?)dinger in nonlinear optical fibers Using the generalized Darboux transformation,an iterative expression of the localized wave solution of N-order for the Schr(?)dinger equation and Lax equation is obtained.Different parameters included in the expression are taken into account.The evolution diagram of the localized wave solution is obtained through numerical simulation,and the dynamic characteristics of the first,second,and third order local wave solutions are analyzed.The results show that different parameters have different effects on the propagation trajectory and local maximum of the envelope function.The research of this article and prospects for future research are summarized in the last.