Research On Analytical Solitions Of Nonlinear Equations In Physical Fields Such As Optical Fiber Communication

Nonlinear equations in physical fields,such as optical fiber commu-nication,are abstracted from various nonlinear phenomena.Especially,the nonlinear Schrodinger equation is used to describe soliton propaga-tion in optical fiber or light propagation in nonlinear optical fiber and planar waveguide.This paper mainly studies the soliton and rogue wave solutions of the Schrodinger equation with variable coefficients,and then analyzes the properties of analytical solutions such as soliton and rogue wave.The main contents of this paper are as follows:In chapter 1,the background of soliton,rogue wave and nonlinear Schrodinger equation are introduced,and the research methods which are used in this paper are introduced,the content and structure of this paper are explained.In chapter 2,the Kundu-Eckhause equation with variable coefficients in inhomogeneous optical fiber is discussed,which describes the propa-gation of ultrashort pulses in inhomogeneous optical fiber.The bilinear form which is different from the existing literature is obtained by Hirota direct method.Based on bilinear equation,the rogue wave solution of the equation is constructed by the KP hierarchy reduction,and the detailed proof is given.Then the influence of variable coefficient on rogue wave is discussed,and the tunneling effect of the rogue wave is also discussed.In chapter 3,the(2+1)-dimensional nonlinear Schrodinger system with variable coefficients in graded index waveguide is discussed,which describes the beam in graded index waveguide with polarization effect.The N-dark-dark soliton and bright-dark soliton solutions of the system are obtained by similarity transformation and KP hierarchy reduction,where N is a positive integer.The propagation and interaction of dark-dark solitons are emphatically discussed graphically.The influence of vari-able coefficients on solitons is also discussed.Under different diffraction coefficients,periodic,cubic and parabolic dark solitons are obtained.Un-der different gain/loss coefficients,periodic and arctangent profile back-ground waves are obtained.In addition,we also discuss the influence of dimensionless beam width coefficient,diffraction coefficient and gain/loss coefficient on soliton and background wave.In chapter 4,the nonlinear Schrodinger system with the negatively coherent coupling in a weakly birefringent fiber is discussed.Through the existing Darboux transformation,we obtain two-soliton solutions and three-soliton solutions,and then obtain four different types of bound soli-tons by parameter control.The interactions between these four types of bound solitons and degenerate/nondegenerate solitons,especially inelas-tic collisions in some cases,are also analyzed graphically.We summarize the contents of this paper and look forward to the future research work in the last chapter.