Dynamics of dark-bright vector solitons in Bose-Einstein condensates

We analyze the dynamics of two-component vector solitons, namely dark-bright solitons, via the variational approximation in Bose-Einstein condensates. The system is described by a vector nonlinear Schrodinger equation appropriate to multi-component Bose-Einstein condensates. The variational approximation is based on a hyperbolic tangent (hyperbolic secant) for the dark (bright) component, which leads to a system of coupled ordinary differential equations for the evolution of the ansatz parameters. We obtain the oscillation dynamics of two-component dark-bright solitons. Analytical calculations are performed for same-width components in the vector soliton and numerical calculations extend the results to arbitrary widths. We calculate the binding energy of the system and find it proportional to the intercomponent coupling interaction, and numerically demonstrate the break up or unbinding of a dark-bright soliton. Our calculations explore observable eigenmodes, namely the internal oscillation eigenmode and the Goldstone eigenmode.