Analyical Study Of The High-Order Coupled Nonlinear Schr?dinger System

There are many nonlinear phenomena widespread in nature.Hence,scientific researchers begin to build corresponding nonlinear models and use these models to describe nonlinear phenomena.Increasingly,the research on nonlinearity has become a more concerned field in the domain of academic.Nonlinear Schr?dinger equation is very important as a part of nonlinear model.It can describe nonlinear phenomena in many fields,including nonlinear optics,Bose Einstein condensation,plasma physics,optical communication and so on.In nonlinear science,soliton theory is a major branch and has important applications in many fields.As the product of nonlinear effect in optics,the special physical properties of optical solitons can be used in optical communication transmission.Thus,the analytical study of soliton solutions of nonlinear Schr?dinger equation has great scientific research value and broad practical application scenarios.In this paper,a high order coupled nonlinear Schr?dinger system is introduced.And the auther introduced a new method called the Hirota bilinear method to solve a variety of soliton solutions of the high-order coupled nonlinear Schr?dinger system model.Next,adjusting the parameters of solitons according to the properties of soliton solutions,we can get the images of the solitons as well as discuss these phenomena The content shall be arranged as follows:In chapter 1,the writer introduces the development and research status of nonlinear science.Then,give a brief introduction of different fields on nonlinear science,including chaos theory,solitons and solitary waves,and reaction-diffusion systems,separately.In addition,optical soliton communication is introduced.Further,the content and structure of this paper are explained.In chapter 2,the author introduces the research methods related to soliton theory,including the direct methods of soliton theory-Hirota transform method,Darboux transform method,Backlaud transform method and Inverse Scattering method.These transformation methods are considerable parts of soliton theory.In Chapter 3,the high-order coupled nonlinear Schr?dinger system with constant coefficients is studied.This equation system can be used to describe soliton propagation in birefringent fibers.The equation is transformed into bilinear form through variable replacement and arrangement by Hirota method.And then,the double soliton solution of the system are solved based on bilinear form.By adjusting the parameters and drawing,the form of the solution of the higher-order coupled nonlinear Schr?dinger system is obtained.After adjusting the parameters of the solution,the interaction between solitons and the transmission form are analyzed.In Chapter 4,the three soliton solutions of high-order coupled nonlinear Schr?dinger systems with constant coefficients are further studied on the basis of Chapter 3.Through symbolic calculation combined with mathematical derivation,the form of three soliton solution is obtained and plotted.At the same time,the parameters are adjusted according to the properties of the three soliton solution,and a new conclusion is obtained:the three soliton solution will appear the phenomena of soliton fusion and fission under certain conditions.Besides,the interaction between solitons in this phenomena are analyzed.In Chapter 5,based on the constant coefficient equation in Chapter 3,the high-order coupled nonlinear Schr?dinger system with variable coefficients is studied.The universality of the system is extended by extending the coefficients of the second-order nonlinear term,dispersion term and high-order effect term from numerical expression to functional expression.The single soliton solution and bimodal single soliton solution are solved,and the effects of different functions on soliton transmission patterns are studied.In Chapter 6,based on the single soliton solution in Chapter 5,the two soliton solutions and three soliton solutions of the variable coefficient nonlinear Schr?dinger equation are solved by transformation setting,and the effects of different intensity functions and wave numbers on the interaction between solitons are discussed respectively.Finally,the seventh chapter summarizes the work of this paper and looks forward to the future research work.