Study On The Perturbed Soliton Of Nonlinear Schr?dinger Equations

Soliton perturbation theory is one of the most significant parts of soliton theory and has a wide range of applications in optics,fluid mechanics,quantum mechanics,etc.In this dissertation,we study the effects on the dynamical property of solitons of the nonlinear Schr?dinger(NLS)equation by adding different perturbations.For bright solitons of the focusing case,based on multiple-scale perturbation expansions,the evolution equations of soliton's amplitude,velocity,initial position and phase have been derived by the adjoint operator method and perturbed conservation laws.For dark solitons of the defocusing case,the evolution equation of soliton's velocity has been derived by the adjoint operator method,while the evolution equations of the background amplitude have been derived by the asymptotic analysis of dark soliton's behavior in infinity.The evolution of shelf and the core soliton have also been obtained.With the shelf cutting the perturbed soliton solutions into interior and external,the evolution equations of initial position and phase can be obtained by perturbed conservation laws of dark solitons.Finally the soliton perturbation theory have been applied into the complexed Ginzburg-Landau equation and the evolution of both bright and dark solitons have been obtained.The study on this dissertation develops the perturbation analysis methods of NLS equation,and reveals the property of moving solitons under perturbations,which enrich the soliton perturbation theory of NLS equation.