Effect of scattering lengths on the dynamics of a two-component Bose-Einstein condensate

TL;DR

This paper investigates how intra- and interspecies scattering lengths influence the stability and existence of solitonic excitations in a two-component Bose-Einstein condensate, providing stability ranges and comparing numerical and analytical results.

Contribution

It offers a detailed analysis of soliton stability in two-component BECs, including stability ranges and the impact of tuning scattering lengths, with both numerical and analytical validation.

Findings

Stability ranges for different soliton pairs are tabulated.

Tuning inter-species scattering length affects soliton stability.

Numerical stability matches analytical predictions and Painlevé analysis.

Abstract

We examine the effect of the intra- and interspecies scattering lengths on the dynamics of a two-component Bose-Einstein condensate, particularly focusing on the existence and stability of solitonic excitations. For each type of possible soliton pairs stability ranges are presented in tabulated form. We also compare the numerically established stability of bright-bright, bright-dark and dark-dark solitons with our analytical prediction and with that of Painlev\'e-analysis of the dynamical equation. We demonstrate that tuning the inter-species scattering length away from the predicted value (keeping the intra-species coupling fixed) breaks the stability of the soliton pairs.