Dark-bright soliton pairs: bifurcations and collisions

TL;DR

This paper studies the static and dynamic behaviors of dark-bright soliton pairs in two-component Bose-Einstein condensates, revealing bifurcations, stability changes, and collision dynamics influenced by intra-species interactions.

Contribution

It identifies and analyzes bifurcations and stability properties of dark-bright soliton pairs as intra-species interactions vary, highlighting new dynamical behaviors.

Findings

Dark-bright soliton pairs bifurcate via transcritical bifurcation.

Stability of antisymmetric and asymmetric states switches at critical points.

Collision dynamics are unaffected by intra-species variation at high energies.

Abstract

The statics, stability and dynamical properties of dark-bright soliton pairs are investigated motivated by applications in a homogeneous system of two-component repulsively interacting Bose-Einstein condensate. One of the intra-species interaction coefficients is used as the relevant parameter controlling the deviation from the integrable Manakov limit. Two different families of stationary states are identified consisting of dark-bright solitons that are either antisymmetric (out-of-phase) or asymmetric (mass imbalanced) with respect to their bright soliton. Both of the above dark-bright configurations coexist at the integrable limit of equal intra- and inter-species repulsions and are degenerate in that limit. However, they are found to bifurcate from it in a transcritical bifurcation. The latter interchanges the stability properties of the bound dark-bright pairs rendering the antisymmetric states unstable and the asymmetric ones stable past the associated critical point (and vice versa before it). Finally, on the dynamical side, it is found that large kinetic energies and thus rapid soliton collisions are essentially unaffected by the intra-species variation, while cases involving near equilibrium states or breathing dynamics are significantly modified under such a variation.