Perturbation theory for bright spinor Bose--Einstein condensate solitons

TL;DR

This paper develops a perturbation theory for bright solitons in spinor Bose-Einstein condensates, allowing analytical prediction of soliton evolution under small deviations from ideal conditions, confirmed by numerical simulations.

Contribution

It introduces an analytical perturbation framework for spinor BEC solitons using Riemann-Hilbert problems, including solutions and stability analysis.

Findings

Solitons are robust against small perturbations.

Soliton velocity, amplitude, and spin populations are preserved.

Small frequency shifts occur due to perturbations.

Abstract

We develop a perturbation theory for bright solitons of the F=1 integrable spinor Bose-Einstein condensate (BEC) model. The formalism is based on using the Riemann-Hilbert problem and provides the means to analytically calculate evolution of the soliton parameters. Both rank-one and rank-two soliton solutions of the model are obtained. We prove equivalence of the rank-one soliton and the ferromagnetic rank-two soliton. Taking into account a splitting of a perturbed polar rank-two soliton into two ferromagnetic solitons, it is sufficient to elaborate a perturbation theory for the rank-one solitons only. Treating a small deviation from the integrability condition as a perturbation, we describe the spinor BEC soliton dynamics in the adiabatic approximation. It is shown that the soliton is quite robust against such a perturbation and preserves its velocity, amplitude, and population of different spin components, only the soliton frequency acquires a small shift. Results of numerical simulations agree well with the analytical predictions, demonstrating only slight soliton profile deformation.