Beating effects of vector solitons in Bose-Einstein condensates

We study the beating effects of solitons in multicomponent coupled Bose-Einstein condensate systems. Our analysis indicates that the period of beating behavior is determined by the energy eigenvalue difference in the effective quantum well induced by solitons, and the beating pattern is determined by the eigenstates of a quantum well, which are involved in the beating behavior. We show that the beating solitons correspond to linear superpositions of eigenstates in some quantum wells, and the correspondence relations are identical for solitons in both an attractive interaction and a repulsive interaction condensate. This provides a possible way to understand the beating effects of solitons for attractive and repulsive interaction cases in a unified way, based on the knowledge of quantum eigenstates. Moreover, our results demonstrate many different beating patterns for solitons in multicomponent coupled condensates, in sharp contrast to the beating dark soliton reported before. The beating behavior can be used to test the eigenvalue differences in certain quantum wells, and more abundant beating patterns are expected to exist in more component-coupled systems.