The Soliton In A Quasi-one-dimensional Bose-Einstein Condensates And It's Application

The Bose-Einstein condensation (BEC) has become a very interesting fron-tier of physics in recent years. Not only can it provide a macro-system, by which quantum mechanics can be studied in another way, but also it will open a wide perspective of application,such as atomic laser and quantum information. The observations of dark and bright matter wave solitons, the study of matter wave solitons have been one of the host issues in the fields of both low-temperature physics and condensated matter physics due to their potential application. In this thesis, by mean-field frame of the Gross-Pitaevskii (GP) equation, the soli-ton in a quasi-one-dimensional Bose-Einstein condensates and it's application are investigated.In the first part, we investigate the exact soliton solutions of the quasi-one-dimensional nonlinear Schrodinger equation with a square-tanh potential. Both the dark soliton and the bright soliton for the repulsive interparticle interaction are found under the existence of the external confining potential. Their stability is examined using analytical method. However, the GP equation is non-integrable, In most circumstances, the exact solutions are difficult to obtain. In the following two chapters, through two approximation methods:the direct perturbation method and the variation method, respectively, we get the approximation solutions of the equation and study the dynamics of BEC.Secondly, We study the formation of a dynamically-stabilized dissipation-managed bright soliton in a quasi-one-dimensional Bose-Einstein condensate by in- cluding an imaginary three-body recombination loss term and an imaginary linear feeding one in the Gross-Pitaevskii equation, trapped in a shallow optical-lattice potential. Based on the direct approach of perturbation theory for the nonlinear Schrodinger equation, we demonstrate that the height (as well as width) of bright soliton may have little change through selecting experimental parameters. This is significant to help in devising experiments.Finally, we present two kinds of exact vector-soliton solutions for the coupled nonlinear Schrodinger equations with time-varying interactions and time-varying harmonic potential. Using the variational approach, we investigate the dynamics of the vector solitons. It is found that the two bright solitons oscillate about slightly and pass through each other around the equilibration state which means they are stable under our model. At the same time, we obtain the opposite situation to the dark-dark solitons.