Nonlinear Waves In A Three-componentbose-einstein Condensate Withpair-transition Effects

Bose-Einstein condensate(BEC)provides a good platform for the investigation of nonlinear waves.Multicomponent BEC can excite more abundant vector nonlinear waves dynamics than one-component system,due to nonlinear coupling effects and particle transition effects between different components.The researches of their excitation mechanisms and dynamical properties are contribute to understand the physical properties of BEC.In this thesis,we use Darboux transformation,linear transformation,linear stability analysis and other mathematical methods to study the spatial-temporal structures and excitation mechanism of nonlinear waves in a three-component BEC with pair-transition(PT)effects.The concrete content are as follows:(1)We obtain kink-dark complex solitons(KDCSs)in a three-component repulsive BEC with PT effects.The classification and excitation conditions of KDCSs are further explored.Although the phase distribution of KDCS appears three times phase jump,the total phase jump value is always .Furthermore,the collision properties of two KDCSs are investigated.It demonstrates some striking particle transition behaviours during their collision processes,while soliton profiles survive after the collision.Particularly,we exhibit the state transition dynamics between a kink and a dark soliton.(2)In the three-component attractive BEC with PT effects,we obtain several complex nonlinear waves.Their collision properties have also been systematically studied.The results show that the collision between soliton and rogue wave is elastic,while the interaction between soliton and Akhmediev breather is inelastic.This is caused by the phase jump before and after the appearance of the Akhmediev breather.Finally,the excitation mechanisms of these complex nonlinear waves have been revealed by linear stability analysis and calculating eigenvectors.The results suggest that they are generated from two different modulation instability branches.The above results indicate that the the emergence of particle transition channels can induce more different types of localized wave structures and intriguing collision behaviors.For the case where there are only pair particle transition channels,the stable localized waves(no particle transition behavior)can be existed,but the collisions between localized waves can induce particle transition behaviors.