Solitary-Wave Solutions Of 2-Component GP Systems With Spin-Orbit Coupling

Spin-orbit coupled ultracold atomic Bose-Einstein condensate is one of the hot topics in physics in the recent decade,its dynamics is described by the GrossPitaevskii equations with spin-orbit coupling,and this kind of equations have received extensive attention in the field of ultracold atomic physics.However,in addition to numerical solutions,exact solutions of these equations are still far from systematic research,the main reason is that the spin-orbit coupling destroys the symmetry and integrability of the system,which makes it become more difficult to find exact solutions.In this thesis,we mainly deal with the spin-1/2 spinorbit coupled Bose-Einstein condensation system.We will consider two(1+1)dimensional models,and a(2+1)-dimensional model which corresponds to the Rashba-Dresselhaus coupling.With the aid of the method of direct ansatz,combining with an integrable reduction of a(1+1)-dimensional system and a technique of separation of functionals for the(2+1)-dimensional system,we provide rich exact solitary-wave solutions for these systems.Especially,for the non-integrable(2+1)-dimensional system,the solutions for collision of solitary waves have been obtained.To our knowledge,it seems that no such kind of result has been reported in the literatures.Based on these exact solutions,the explicit expression of spin polarized vector corresponding to the spinor Bose-Einstein condensate systems are presented,the spin dynamics and the phenomena of quantum magnetization are characterized.Our results can be applied to theoretical study of the spinor BoseEinstein condensate,and are helpful for deeply understanding how the spin-orbit coupling affects the dynamics of the spinor Bose-Einstein condensates and their quantum magnetization behavior.This paper provides an interdiscipline study of soliton theory and ultracold atoms system.