Analytical Study Of High-Order Nonlinear Schrodinger Model In Optical Fiber Communication

There are many complex nonlinear phenomena in our life,and the study of these nonlinear situations can better promote the development of science and technology.At present,the main research direction of nonlinear is soliton,chaos and fractal.Since 1970,solitons have received extensive attention and research.Since solitons can carry out long-distance communication without changing their shape,they have great research value in the field of optical fiber communication.Nonlinear schrodinger equation is an important model of nonlinear,it can well describe the optical,plasma physics,optical communications,and other fields of some nonlinear situation,with the acceleration development of research,present a lot of high order nonlinear phenomena,therefore,to study the higher order nonlinear schrodinger equation both in theoretical and practical application has great significance.The main content of this paper is to use the Hirota bilinear method to solve the soliton solutions of several high-order nonlinear Schrodinger equation models,and then by drawing images to intuitively discuss and analyze the interaction between the solitons.The content of this paper includes:(1)This paper first introduces some background and nonlinear models of nonlinear science,then introduces some development history and current research status of soliton theory,and finally gives a specific introduction to optical soliton.(2)Some common methods used to solve nonlinear equations are introduced.Firstly,the inverse scattering method,Backlund transformation method,Darb transformation method and Painleve analysis method are briefly introduced.Next,the Hirota bilinear method which will be used in this paper is introduced in detail,including its principle and some transformation methods.(3)The variable coefficient nonlinear Schrodinger equation with a fourth-order model is selected to explore some conditions of solitons when optical pulses propagate in non-uniform fiber.The Hirota bilinear method is used for analytical solution to obtain the dark three-soliton solution.Based on the obtained solution,the transmission and interaction of solitons are discussed.Some properties of solitons can be obtained by selecting some suitable parameters.The periodic transmission can be obtained by changing the dispersion coefficient,and the amplitude can be controlled by controlling parameters.In addition,a V-shaped soliton graph is proposed,and the direction of transmission can be changed by controlling the parameters.In addition,some cases of front collision and overtaking collision of dark solitons are studied.These results may be of reference value to the research of all-optical switches.(4)The model is selected as a fifth-order nonlinear Schrodinger equation with variable coefficients,and solved analytically by Hirtoa bilinear method to obtain the explicit single soliton solution and explicit double soliton solution.By controlling the parameters,we can get some properties between some solitons.In the study of single solitons,the amplitude and intensity of solitons can be controlled by controlling parameters.In the study of double solitons,we can get a certain periodicity of soliton transmission,two collided solitons attract each other and then repel each other,the direction of soliton transmission and the intensity of interaction between the solitons can be changed by using parameters,these results may be of some reference value to the application of optical path control.(5)The model is selected as a nonlinear Schrodinger equation with variable coefficients of the fifth order.The Hirota bilinear method is used to solve the equation analytically.The bright three soliton solutions of the equation are obtained,and the interaction of some solitons during transmission is discussed.By controlling the parameters,we can control the amplitude of the soliton pulse,the interaction between the solitons will also change,and the soliton transmission has a certain periodicity.Some phenomena about the fusion of solitons are also discussed.Two solitons can be fused into one soliton for transmission by selecting appropriate parameters.These results will be helpful to some applications of optical switches and fiber lasers.