Propagation Characteristics And Manipulation Of Local Wave Packets In Inhomogeneous Optical Fiber Systems

With the rapid development of scientific revolution,the study of nonlinear science is also accelerating.The study of local wave packet,which refers to the wave formed by the superposition of several harmonics under certain conditions and has local properties is a branch of nonlinear science.The unique properties of optical solitons and breathers make them of profound research significance in various fields,so the transmission characteristics of optical solitons and breathers in optical fiber are widely studied.It is well known that the generalized nonlinear Schr?dinger equation can be used to describe the local wave packet.In this paper,the generalized nonlinear Schr?dinger equation is taken as the model,and the exact solution forms of optical soliton and breathers are obtained by analytical solution method,and their dynamic characteristics are studied.The main research achievements and innovations are as follows:First,the nonlinear Schr?dinger equation with third-order dispersion,nonlinear effect,self-steepening effect and Raman effect is studied based on the nonlinear system propagating femto-second soliton pulses.Using mathematical method to solve this equation,the periodic waves transmitted in homogeneous optical fiber are obtained.Then,the extended nonlinear Schr?dinger equation with linear potential in the inhomogeneous system as a model is studied,and the mathematical expression of optical solitons by appropriate similarity transformation method is given.On this basis,the dynamic behaviors of optical solitons in periodic and exponential dispersive fiber systems are discussed separately.Second,the nonlinear Schr?dinger equation with third-order dispersion,fourth-order dispersion,nonlinear effect,self-steepening effect and Raman effect is studied based on the nonlinear system propagating femto-second soliton pulses.A class ofsech~2 soliton and dipole soliton transmitted in homogeneous fiber are constructed.By similarity transformation method,these constructed optical solitons are introduced into inhomogeneous optical fibers.On this basis,the parameter modulation of self-similar dipole solitons in exponential and periodic dispersive fiber systems is discussed in detail.The results show that the dipole solitons exhibit different propagation dynamics with different forms of fourth-order dispersion and nonlinear effects.The amplitude and trajectory of self-similar dipole solitons can be modulated by manipulating parameters.Third,based on non-local nonlinear systems in homogeneous optical fibers,the first order self-similar breather in homogeneous optical fibers is studied by means of similarity transformation method.And the dynamics of self-similar breather in different dispersion optical fiber systems are analyzed graphically and discussed in detail.It is found that by adjusting the parameters of self-similar breather solution,some special phenomena can be clearly observed and a variety of dynamic behaviors can be displayed.