# Matter-Wave Bright Solitons with a Finite Background in Spinor Bose-Einstein Condensates

## TL;DR

This paper explores the properties of bright matter-wave solitons with finite backgrounds in spinor Bose-Einstein condensates, revealing their classifications, collision behaviors, and potential for robust quantum applications.

## Contribution

It introduces explicit one-soliton solutions with finite backgrounds in spinor BECs using inverse scattering, classifies solitons into two types, and analyzes their collision dynamics.

## Key findings

- Two soliton types: domain-wall and phase-shift.
- Confirmed spin-mixing during collisions.
- Results align with previous soliton studies.

## Abstract

We investigate dynamical properties of bright solitons with a finite background in the F=1 spinor Bose-Einstein condensate (BEC), based on an integrable spinor model which is equivalent to the matrix nonlinear Schr\"{o}dinger equation with a self-focusing nonlineality. We apply the inverse scattering method formulated for nonvanishing boundary conditions. The resulting soliton solutions can be regarded as a generalization of those under vanishing boundary conditions. One-soliton solutions are derived in an explicit manner. According to the behaviors at the infinity, they are classified into two kinds, domain-wall (DW) type and phase-shift (PS) type. The DW-type implies the ferromagnetic state with nonzero total spin and the PS-type implies the polar state, where the total spin amounts to zero. We also discuss two-soliton collisions. In particular, the spin-mixing phenomenon is confirmed in a collision involving the DW-type. The results are consistent with those of the previous studies for bright solitons under vanishing boundary conditions and dark solitons. As a result, we establish the robustness and the usefulness of the multiple matter-wave solitons in the spinor BECs.