Dark–dark soliton breathing patterns in multi-component Bose–Einstein condensates

Abstract

In this work, we explore systematically various SO(2)-rotation-induced multiple dark–dark (DD) soliton breathing patterns obtained from stationary and spectrally stable multiple dark–bright (DB) and DD waveforms in trapped one-dimensional, two-component atomic Bose–Einstein condensates. The stationary states stemming from the associated linear limits (as the eigenfunctions of the quantum harmonic oscillator problem) are parametrically continued to the nonlinear regimes by varying the respective chemical potentials, i.e. from the low-density linear limits to the high-density Thomas–Fermi (TF) regimes. We perform a Bogolyubov–de Gennes spectral stability analysis to identify stable parametric regimes of these states, finding a wide range of stability intervals in the TF regimes for all of the states considered herein. Upon applying an SO(2)-rotation to stable steady states, one-, two-, three-, four-, and many DD soliton breathing patterns are observed in the numerical simulations. Furthermore, analytic solutions up to three DB solitons in the homogeneous setting, and three-component systems are also investigated.