1-Soliton dynamics of the perturbed nonlinear Schroedinger's equation.

摘要

This thesis is concerned with the analytical and numerical study of the perturbed Nonlinear Schrodinger's Equation that governs the propagation of pulses through an optical fiber. The perturbation terms that were considered here are a combination of the Hamiltonian as well as the non-Hamiltonian types. The analytical study is made by using the technique of the Multiple Scale Perturbation Expansion, and the results have been supported by numerical simulations of the governing equations.;This dissertation is divided into three chapters. In the first chapter a formal derivation of the Nonlinear Schrodinger's Equation is carried out. Also the method of deriving the perturbation terms of the Nonlinear Schrodinger's Equation is given and relevant references are cited.;In the second chapter, the known properties of the Nonlinear Schrodinger's Equation are revisited. Also the existing properties of the perturbed Nonlinear Schrodinger's Equation are reviewed. Moreover the limitations of the known methods of analysis of the perturbed Nonlinear Schrodinger's Equation are given. Finally some reference has been made to the existing results obtained by others together with their limitations and drawbacks. This gives us a motivation to study the perturbed Nonlinear Schrodinger's Equation by the method of Multiple Scale Perturbation Expansion.;Finally in the third chapter, the Multiple Scale Perturbation analysis was carried out to obtain the results that are a generalization of the existing results. Moreover it is shown that this is a general method of analysis of the perturbed Nonlinear Schrodinger's Equation containing both Hamiltonian as well as non Hamiltonian terms. The adiabatic variation of the soliton parameters like the soliton amplitude, the soliton frequency and the soliton velocity are obtained as the solvability criterion of the Multiple Scale perturbation expansion. The results thus obtained matches and generalizes of the existing results. Moreover the numerical runs have been obtained support the analysis that was developed.