Modulating The Amplitude Of Solitons In Low-Dimensional Bose System

Since the dark soliton in a quasi-one dimensional (cigar-shaped) condensate was observed in 1999, the study of dynamics properties of solitons in Bose Einstein condensates (BECs) has become one of the hot subjects in science region, such as condensate physics, low-temperature physics and so on. BEC trapped in different external potential will result in different nonlinear phenomena. For example, BEC trapped in external harmonic potential, there exists dark soliton in condensates with interatomic repulsive interaction, and there occurs bright soliton when interatomic interaction is attractive. If the condensate is trapped in hyperbolic functions potential, there exhibits dark soliton in condensates when interatomic interaction is attractive, and there appears bright soliton when interatomic interaction is repulsive. So far, it has been realized that controlling the scattering length of atoms in condensate via Feshbach resonance. Thereby it is an interesting subject that the effect of interatomic interaction on dynamics properties of solitons is considered in BEC. Based on the Gross-Pitaevskii equation which can describe a number of properties of BEC under the mean-field approximate, we have studied analytically the behaviors of soliton in quasi-one and quasi-two dimensional condensate in the thesis, by use of the nonlinear perturbation theory, and obtained series of significative result. The article is organized as follows:In chapter 1, we introduce the basic theory, the general study situation, the scientific sense of BEC and the method and the content which we study in article.It has been realized that the scattering length of atoms in condensate can be controlled by Feshbach resonance, consequently the interatomic interaction can also been controlled. So in chapter 2, we study analytically the effect of scattering length on the dynamics of soliton in quasi-one dimensional BEC. It is shown that, when the scattering length increased via Feshbach resonance, the black soliton transforms into the stable gray soliton in condensates; and when the scattering length decreased by Feshbach resonance, the gray soliton turns into the black soliton. Base on currently experimental conditions, we propose experimental protocols to realize the stable exchange between black and gray solitons.In chapter 3, we study the nonlinear dynamics of a quasi-two dimensional condensate. It is found that, there is a dark soliton in condensate when the interatonic interaction is repulsive; the dark soliton is instability with the time, it evolves into ring dark soliton with a small amplitude; the shallow ring dark soliton will become dynamic stabilization.Finally, we give a simple summary and prospect about solitons of BEC.