# Stability and dynamics of dark-bright soliton bound states away from the integrable limit

## TL;DR

This paper investigates the stability and dynamics of dark-bright soliton pairs in two-component Bose-Einstein condensates, especially how they behave when interaction parameters deviate from the integrable limit, revealing stable regimes, bifurcations, and symmetry-breaking phenomena.

## Contribution

It provides a detailed analysis of dark-bright soliton pairs away from the integrable limit, identifying stability regions, bifurcations, and symmetry-breaking states in atomic Bose-Einstein condensates.

## Key findings

- Dark-bright soliton pairs are stable over a wide parameter range.
- Instabilities lead to redistribution of bright density and symmetry-breaking.
- Long-term dynamics include stable, unstable, and asymmetric states.

## Abstract

The existence, stability, and dynamics of bound pairs of symbiotic matter waves in the form of dark-bright soliton pairs in two-component mixtures of atomic Bose-Einstein condensates is investigated. Motivated by the tunability of the atomic interactions in recent experiments, we explore in detail the impact that changes in the interaction strengths have on these bound pairs by considering significant deviations from the Manakov (integrable) limit. It is found that dark-bright soliton pairs exist as stable configurations in a wide parametric window spanning both the miscible and the immiscible regime of interactions. Outside this parameter interval two unstable regions are identified and are associated with a supercritical and a subcritical pitchfork bifurcation, respectively. Dynamical manifestation of these instabilities gives rise to a redistribution of the bright density between the dark solitons, and also to symmetry-broken stationary states that are mass imbalanced (asymmetric) with respect to their bright soliton counterpart. The long-time dynamics of both the stable and the unstable balanced and imbalanced dark-bright soliton pairs is analyzed.