Study On The Multi-soliton Solutions And Their Transmission Characteristics Of The Coupled Nonlinear Schr(?)dinger Equation

Due to the balance between group velocity dispersion and self-frequency shift modulation,optical solitons can travel long distances in the fiber without changing the shape.Because of this characteristic,solitons can be transmitted over large distances and large capacity in optical fiber communication systems.It can be applied in many fields and has become the content of many scholars' research.The nonlinear Schr?dinger equation is an ideal model for describing the soliton transmission.It is a very important nonlinear evolution equation.As the research progresses,the nonlinear Schr?dinger equation is extended to variable coefficients,complex coefficients,high-dimensional,high-order,non-local and fractional equations include various types of physical effects.By studying various equations,we can better understand many nonlinear phenomena.Therefore,it is very important to study the transmission characteristics of soliton and some potential applications through the nonlinear Schr?dinger equation.It has certain theoretical guiding significance for the development of soliton theory and the development of different application fields.This article mainly introduces the research background and progress of nonlinear Schr?dinger equation,the origin and research progress of solitons and breathers.Based on these,the N-soltion solutions and their interactions are studied by using the Hirota bilinear method.The specific research contents are as follows:(1)Based on the self-focusing generalized coupled nonlinear Schr?dinger equation,which includes self-phase modulation,cross-phase modulation,and four-wave mixing effects,the 4-bright-bright soliton solution of the equation is obtained by using the Hirota bilinear method.The soliton collision dynamics have been studied in detail.The results show that the imaginary part of the eigenvalue affects the speed and pulse width of the soliton,and the real part of the eigenvalue change the amplitude of the soliton.(2)Based on the self-defocusing generalized coupled nonlinear Schr?dinger equation including the four-wave mixing effect,the 4-dark-dark soliton solution of the equation is obtained bt using the Hirota bilinear method.The value range of different parameters are analyzed,and numerical research is performed.The results show that 4-dark solitons,3-dark solitons and dark-soliton-anti-dark soliton combinations can be obtained by adjusting of parameters,but the interaction between solitons is still an elastic collision.(3)Based on the variable coefficient coupled nonlinear Schr?dinger equation,the 2-soliton solution is obtained by using Hirota bilinear method.The solution includes three bright soliton components and one dark soliton component.When the eigenvalue of the soliton is complex,two elastic collision conditions are obtained that one is the conventional elastic collision and the other is the quasi-elastic collision with a bright soliton disappearing.When soliton eigenvalues are constant,bound state solitons can be obtained.The results show that reasonable selection of parameters can obtain the two-soliton solutions for elastic collisions,inelastic collisions,and bound state transmission.