Influence Of Higher-order Effects On The Propagation Characteristics Of N-soliton Solutions Of The Coupled Nonlinear Schr(?)dinger Equation

Optical solitons are formed by the interaction of two basic physical phenomena in optical fibers,namely group velocity dispersion and self-phase modulation.Because of the balance between the two,the optical solitons can maintain their shape and speed over long distances in the fiber.It is precisely because of this characteristic that optical solitons have important application prospects in the field of optical communication.The propagation of optical solitons in optical fibers can be described by the nonlinear Schr(?)dinger equation and its various modified forms.With the development of science and technology and the deepening of research,there have been a lot of studies on the propagation characteristics of nonlinear Schr(?)dinger equation and its different forms of soliton solutions.However,the influence of gain and higher-order effects on the propagation characteristics of N-soliton solutions of coupled nonlinear Schr(?)dinger equation are seldom studied.Therefore,based on the coupled nonlinear Schr(?)dinger equation,this paper mainly studies the following contents:Firstly,based on the coupled nonlinear Schr(?)dinger equation and the N-soliton solution obtained by the Hirota method,the soliton propagation characteristics are discussed in detail.The results show that the system parameters a,b and c mainly affect the amplitude of N-soliton solution.The real part of the solution parameter6)₄)has a certain effect on the pulse width and amplitude,and the imaginary part of6)₄)directly determines the migration velocity of the soliton.The change of solution parameterwill cause the energy between soliton solutions to be redistributed,so thatandcomponents will not be identical.Secondly,by adding the gain term to the coupled nonlinear Schr(?)dinger equation,the effects of different gain forms on the propagation characteristics of soliton solutions are investigated numerically by using the split-step Fourier method.The results show that the solitons have different pulse shapes with different gain forms,and the amplitude and oscillation period of the pulse vary with the change of parameters.Finally,based on the coupled nonlinear Schr(?)dinger equation including self-steepening effect and self-frequency shift effect,the influence of these two effects on the propagation characteristics of soliton solutions are investigated numerically.The results show that both self-steepening effect and self-frequency shift effect cause solution deflection in the transmission process.And the redistribution of energy causes the amplitude to change.For the soliton solution with the breathing-like structure,as self-steepening effect and self-frequency shift effect gradually increasing,the high-order solitons will eventually split into several solitons with different amplitudes and different propagating velocities.