# Normal mode oscillations of a nonlocal composite matter wave soliton

## TL;DR

This paper demonstrates the existence of stable three-soliton bound states in a nonlocal Bose-Einstein condensate, analyzes their normal modes, and compares their oscillation frequencies, revealing unique asymmetric mode characteristics.

## Contribution

It introduces the concept of stable three-soliton molecules with nonlocal interactions and investigates their normal mode oscillations using variational and numerical methods.

## Key findings

- Stable three-soliton bound states are demonstrated.
- The interaction potential is of molecular type, attractive at long range and repulsive at short range.
- Asymmetric mode frequency is smaller than symmetric mode frequency.

## Abstract

The existence of stable bound states of three solitons in a Bose-Einstein condensate with nonlocal interactions is demonstrated by means of variational approach (VA) and numerical simulations. The potential of interaction between solitons derived from VA is shown to be of molecular type, i.e. attractive at long distances and repulsive at short distances. Normal modes of a three-soliton molecule are investigated by computing small amplitude oscillations of individual solitons near their equilibrium positions. Symmetric and asymmetric stretched states of the molecule are prepared and used as initial conditions in numerical simulations of the nonlocal Gross-Pitaevskii equation. As opposed to usual triatomic molecules, we find that the frequency of the asymmetric mode of a three-soliton molecule is smaller than the one of the symmetric mode. Possible experimental settings for the observation of these results are briefly discussed.