Properties Of Solitons In Bose-Einstein Condensate And Magnetic Films

Solitons show unique properties and high potential for applications and, hence, have been one of the most exciting topics in modern nonlinear science. This thesis is devoted to the theoretical investigation of soliton dynamics in Bose-Einstein Condensates (BECs) and magnetic thin films. The work is based on the nonlinear Schr(?)dinger equation (NLSE) and the use of the variational appraoach and the split-step Fourier method.The thesis consists of three main parts. In the first part, the nonlinear Schr?dinger equation (NLSE) is briefly introduced. This equation can be used to describe the evolution dynamics of both the solitons in the BEC systems and the microwave magnetic envelope (MME) solitons in magnetic films. The variational approach and the Split-step Fourier method are also introduced. The first one is a typical theoretical tool for the analyses of the soliton solution of the NLSE under restricted conditions. The later one is often used for the numerical simulation of the NLSE.From both the fundamental and practical points of view, the stability of solitons in a nonlinear system is critical. The second part of the thesis is devoted to the stability of the BEC solitons and its control methods as well as the physical behaviors of BEC solitons under a variety of different trapping potentials. Three main works are as follows.One work is on the dynamics of one and several BEC solitons in a typical trap that is perturbed by a local impurity. It is found that the dynamics of the solitons in such a trap strongly depends on the properties of the trapping potential, the parameters of the BEC system, and the other initial conditions. It is also found that an appropriate potential perturbation can not only enhance the stability of the solitons, but also can be used to control the evolution of the solitons.The second work is on the evolution of single and coupled BEC solitons. In this work, the concept of effective potential was introduced to the analyses of the BEC solitons. The effective potential for the external trapping potential and that from the interaction of coupled solitons were obtained. From these effective potentials, one can know the evolution dynamics of the BEC solitons and the interaction of the coupled solitons. One can also know the thresholds for the stationary and self-trapping states of the solitons. In addition, one can know the properties for the atom transfer between coupled solitons.The effects of three-body interactions on BEC soliton dynamics are also studied. It is found that even a weak three-body interaction can lead to a significant chang in soliton dynamics. The dynamics of 2D cake-shaped solitons was also studied. This work was done for a cylindral potential modified by an optical lattice. It is found the introduction of an optical lattice can not only enhance the stability of the solitons in the direction of the opdtical lattice, but also improve the stability in other directions.The third part focuses on the MME solitons in magnetic thin films. The propagation dynamics of narrow MME solitons was studied. This work was performed with the use of a NLSE that contained high-order dispersion terms. It is found that, under certain conditions, the nonlinear systems with high-order dispersion can support narrow MME solitons. It is also found that, with high order dispersion, the soliton dynamics is independent of the soliton initial phase. Strong third-order dispersion effect can also lead to the break-up of an MME soliton, but this break-up can be controlled through the introduction of an initial phase.