Systematic vector solitary waves from their linear limits in one-dimensional $n$-component Bose-Einstein condensates

TL;DR

This paper develops a systematic method to construct and analyze vector solitary waves in multi-component Bose-Einstein condensates, demonstrating their stability and dynamic behaviors across different density regimes.

Contribution

It introduces a continuation approach from linear limits to nonlinear regimes for multi-component BECs, enabling the systematic construction and stability analysis of vector solitary waves.

Findings

All considered states can be stabilized in the Thomas-Fermi regime.

The method applies to 3-5 component BECs and can be extended to higher dimensions.

Dynamic behaviors include $SU(n)$-rotation-induced and driving-induced phenomena.

Abstract

We systematically construct a series of vector solitary waves in harmonically trapped one-dimensional three-, four-, and five-component Bose-Einstein condensates. These stationary states are continued in chemical potentials from the analytically tractable low-density linear limit of respective states, as independent linear quantum harmonic oscillator states, to the high-density nonlinear Thomas-Fermi regime. A systematic interpolation procedure is proposed to achieve this sequential continuation via a trajectory in the multi-dimensional space of the chemical potentials. The Bogolyubov-de Gennes (BdG) spectra analysis shows that all of the states considered herein can be fully stabilized in suitable chemical potential intervals in the Thomas-Fermi regime. Finally, we present some typical $SU(n)$-rotation-induced and driving-induced dynamics. This method can be extended to higher dimensions and shows significant promise for finding a wide range of solitary waves ahead.