Exact temporal evolution of the two-species Bose-Einstein condensates
Cong Zhang, Zhi-Hai Zhang, and Shi-Jie Yang
TL;DR
This paper derives exact stationary and time-evolving solutions for two-species Bose-Einstein condensates in one dimension, revealing complex and soliton solutions with spatiotemporal periodicity, based on coupled Gross-Pitaevskii equations.
Contribution
It introduces new exact analytical solutions for two-species BECs, including time-dependent solutions using SU(2) symmetry, advancing understanding of their dynamics.
Findings
Derived three types of complex stationary solutions
Obtained analytical time-evolving solutions with periodicity
Identified soliton limits of the solutions
Abstract
We construct exact stationary solutions to the one-dimensional coupled Gross-Pitaevskii equations for the two-species Bose-Einstein condensates with equal intraspecies and interspecies interaction constants. Three types of complex solutions as well as their soliton limits are derived. By making use of the SU(2) unitary symmetry, we further obtain analytical time-evolving solutions. These solutions exhibit spatiotemporal periodicity.
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