Dark-bright soliton interactions beyond the integrable limit

TL;DR

This paper provides a systematic theoretical analysis of dark-bright soliton interactions in Bose-Einstein condensates beyond the integrable limit, revealing fixed points, instabilities, and bifurcations through variational methods.

Contribution

It introduces a variational approach to analyze dark-bright soliton interactions beyond the integrable regime, identifying stability and bifurcation phenomena.

Findings

Existence of fixed points for out-of-phase bright solitons.

Exponential instability and bifurcation leading to soliton splitting.

Absence of bound states for in-phase bright solitons despite variational predictions.

Abstract

In this work we present a systematic theoretical analysis regarding dark-bright solitons and their interactions, motivated by recent advances in atomic two-component repulsively interacting Bose-Einstein condensates. In particular, we study analytically via a two-soliton ansatz adopted within a variational formulation the interaction between two dark-bright solitons in a homogeneous environment beyond the integrable regime, by considering general inter/intra-atomic interaction coefficients. We retrieve the possibility of a fixed point in the case where the bright solitons are out of phase. As the inter-component interaction is increased, we also identify an exponential instability of the two-soliton state, associated with a subcritical pitchfork bifurcation. The latter gives rise to an asymmetric partition of the bright soliton mass and dynamically leads to spontaneous splitting of the bound pair. In the case of the in-phase bright solitons, we explain via parsing the analytical approximations and monitoring the direct dynamics why no such pair is identified, despite its prediction by the variational analysis.