Solutions of multi-component NLS models and spinor Bose-Einstein condensates

TL;DR

This paper investigates multi-component nonlinear Schrödinger models describing spinor Bose-Einstein condensates with hyperfine structures F=1 and F=2, deriving integrable cases and soliton solutions using inverse scattering and dressing methods.

Contribution

It introduces specific multi-component NLS models for spinor BECs, identifies their integrable cases, and constructs soliton solutions via a modified dressing procedure.

Findings

Identification of integrable multi-component NLS models for F=1 and F=2 BECs.

Construction of various soliton solutions using inverse scattering and dressing methods.

Connection of models to symmetric spaces of BD.I-type.

Abstract

A three- and five-component nonlinear Schrodinger-type models, which describe spinor Bose-Einstein condensates (BEC's) with hyperfine structures F=1 and F=2 respectively, are studied. These models for particular values of the coupling constants are integrable by the inverse scattering method. They are related to symmetric spaces of BD.I-type SO(2r+1)/(SO(2) x SO(2r-1)) for r=2 and r=3. Using conveniently modified Zakharov-Shabat dressing procedure we obtain different types of soliton solutions.