Analytical Solutions For The System Of The Spin-orbit-coupled Spinor BEC

This thesis investigates the following Gross-Pitaevskii system which describes the dynamics of the spin-orbit coupled spinor Bose-Einstein condensates4) 1= [-122+((80+ (82)(|1|2+ |0|2)+((80- (82) |-1|2] 1+ (8220*-1+√20,4) 0= [-122+(c0+ c2)(|1|2+ |-1|2) + c0|0|2]0+2 (82*01-1-√2(1- -1),4) -1 = [-122+((80+ (82)(|-1|2+ |0|2)+((80- (82) |1|2] -1 + (82 20*1-√20.By virtue of two kinds of transformation, we reduce the system to the standard scalar Schrodinger equation and a system of ordinary differential equations respectively,and then we get rich analytical solutions, including periodic solutions and solitary solutions. These solutions can be used to discuss the evolution of the dynamics and the phenomena of the quantum magnetization for the condensates. We also present some novel solutions for the decoupling( = 0) case.