# Non-degenerate Bound State Solitons in Multi-component Bose-Einstein Condensates

## TL;DR

This paper systematically studies non-degenerate bound state solitons in multi-component Bose-Einstein condensates using Darboux transformation, revealing their properties, interactions, and potential applications in quantum physics.

## Contribution

It introduces a novel analytical method to derive exact bound state soliton solutions and uncovers their unique properties and interactions in multi-component BECs.

## Key findings

- Bright solitons with nodes are excited bound eigen-states.
- Bound state solitons are induced by incoherent inter-component interactions.
- Interactions between bound state solitons are generally inelastic.

## Abstract

We investigate non-degenerate bound state solitons systematically in multi-component Bose-Einstein condensates, through developing Darboux transformation method to derive exact soliton solutions analytically. In particular, we show that bright solitons with nodes correspond to the excited bound eigen-states in the self-induced effective quantum wells, in sharp contrast to the bright soliton and dark soliton reported before (which usually correspond to ground state and free eigen-state respectively). We further demonstrate that the bound state solitons with nodes are induced by incoherent interactions between solitons in different components. Moreover, we reveal that the interactions between these bound state solitons are usually inelastic, caused by the incoherent interactions between solitons in different components and the coherent interactions between solitons in same component. The bound state solitons can be used to discuss many different physical problems, such as beating dynamics, spin-orbital coupling effects, quantum fluctuations, and even quantum entanglement states.