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We investigate the expansion dynamics of a Bose-Einstein condensate thatconsists of two components and is initially confined in a quasi-one-dimensionaltrap. We classify the possible initial states of the two-component condensateby taking into account the non-uniformity of the distributions of itscomponents and construct the corresponding phase diagram in the plane ofnonlinear interaction constants. The differential equations that describe thecondensate evolution are derived by assuming that the condensate density andvelocity depend on the spatial coordinate quadratically and linearly,respectively, what reproduces the initial equilibrium distribution of thecondensate in the trap in the Thomas-Fermi approximation. We obtainedself-similar solutions of these differential equations for several importantspecial cases and wrote out asymptotic formulas describing the condensatemotion on long time scales, when the condensate density becomes so low that theinteraction between atoms can be neglected. The problem on the dynamics ofimmiscible components with the formation of dispersive shock waves was alsoconsidered. We compare the numerical solutions of the Gross-Pitaevskiiequations with their approximate analytical solutions and study numerically thesituations when the analytical method admits no exact solutions.

journal of experimental and theoretical physics

Expansion Dynamics of a Two-Component Quasi-One-Dimensional  Bose-Einstein Condensate: Phase Diagram, Self-Similar Solutions, and  Dispersive Shock Waves