Systematic solitary waves from their linear limits in two-component Bose-Einstein condensates with unequal dispersion coefficients

TL;DR

This paper constructs and analyzes vector solitary waves in two-component Bose-Einstein condensates with unequal dispersion coefficients, revealing new solution series and stability properties through numerical continuation from linear limits.

Contribution

It introduces a systematic numerical method to find and analyze new vector solitary wave solutions in BECs with unequal dispersion, extending known solutions and exploring their stability.

Findings

New series of vector solitary waves identified.

Most states are unstable but can be stabilized.

Solutions include dark-anti-dark and dark-multi-dark waves.

Abstract

We systematically construct vector solitary waves in harmonically trapped one-dimensional two-component Bose-Einstein condensates with unequal dispersion coefficients by a numerical continuation in chemical potentials from the respective analytic low-density linear limits to the high-density nonlinear Thomas-Fermi regime. The main feature of the linear states herein is that the component with the larger quantum number has instead a smaller linear eigenenergy, enabled by suitable unequal dispersion coefficients, leading to new series of solutions compared with the states similarly obtained in the equal dispersion setting. Particularly, the lowest-lying series gives the well-known dark-anti-dark waves, and the second series yields the dark-multi-dark states, and the following series become progressively more complex in their wave structures. The Bogoliubov-de Gennes spectra analysis shows that most of these states are typically unstable, but they can be long-lived and most of them can be fully stabilized in suitable parameter regimes.