The Theory Of Soliton Perturbations Of Nonlinear Schr(?)dinger Equation And It's Application In Optical Fibre Communication

Nonlinear Schr(o|¨)dinger equation (NLSE) is one of the most important equation with universal significance of modern science.Its soliton solution has been applied in many fields of physics. In real nonlinear systems, additional effects appear in the standard soliton equation inevitably. so, the soliton perturbation theory of NLSE is very important in application field.It mainly includes the follow two kinds: the theory which based on the inverse scattering transformation (IST) and the semi-direct method where the squared Jost solutions(which are the special solutions of the NLSE by using the IST ) are employed as the basis for perturbation expansion. Although both of the two method have important learning value,but they are just fit for integral systems and can not be grasped by most people because of the complex calculation.Professor Jiaren Yan,who is my thesis supervisor,had developed a direct approach of the soliton perturbation theory based on separating variable technique.It is applicable to both integrable and unintegrable systems. Especially,the difficult perturbation problem of dark soliton can be successfully solved by this method.In this paper, we discuss some significant perturbations(two-photon absorption, gain, spectral filtering et.al.) in the optical fibre communication system using the direct method. Our work may give some theory reference value to enhance the information precision of the long distance communication by controlling system parameters. At present, the optical fibre communication is considered as the preceding subject which has the most bright future.Thereby, the application of the theory of soliton perturbations in optical fibre communication has significant scientific research value. Besides, they can enrich the soliton perturbation theory of professor Yan and offer some important examples.This thesis consists of five chapters. The history of soliton and nonlinear optic are introduced in chapter one.What's more,the NLSE is derived in the case of the balance of group-velocity dispersion and nonlinear effects.Some important nonlinear effects was discussed in chapter two. The dynamics of dark and bright soliton in optical fibre were studied in Chapter three and four respectively by using the perturbation theory of NLSE.We summarize our work and discuss its prospect in chapter five.