Analytical Solutions Of (2+1)-dimensional Spin-1 BEC System With Rashba-Dresselhaus Spin-orbit Coupling

Spin-orbit coupling is a relativistic effect,and the realization of artificial spinorbit coupling in Bose-Einstein condensates provides a new way for quantum simulation and manipulation.In recent years,the study of novel physical phenomena based on spin-orbit coupling in ultracold atomic systems has become one of the hot spots,among which the study of soliton states of Bose-Einstein condensates with spin-orbit coupling is a subject of great concern in this field.Under the mean-field theory,one can use Gross-Pitaevskii equations to describe the dynamics of Bose-Einstein condensates.This thesis mainly considers the 3-component Gross-Pitaevskii system of(2+1)-dimensional spin-1 Bose-Einstein condensates with Rashba-Dresselhaus type spin-orbit coupling.The equations are solved exactly.Under appropriate conditions,by using the method of separation of two functions and the single function reduction,combined with the direct ansatz,various types of soliton solutions of the equations are obtained,including the types of antikink-antikink-antikink solution,antikink-kink-antikink solution,Wbright-W solution,bright-W-bright solution,dark-dark-dark solution,oscillating bright-bright-bright solution,oscillating dark-dark-dark solution,periodic solutions,and collision soliton solutions.In addition,in the case of opposite Rashba and Dresselhaus couplings,a transformation is found that can convert the GrossPitaevskii system into the single standard(2+1)-dimensional cubic Schrodinger equation.In this way,rich solutions of the Gross-Pitaevskii system,especially the Kuznetsov-Ma breather,the Akhmediev breather,Peregrine soliton,and Nsoliton of travelling wave type,can be obtained by employing the known results of the(2+1)-dimensional cubic Schrodinger equation.Our results are helpful to the deep understand of the correspond physical systems.