# Stability of single and multiple matter-wave dark solitons in collisionally inhomogeneous Bose-Einstein condensates

## TL;DR

This paper investigates the spectral stability of single and multiple matter-wave dark solitons in Bose-Einstein condensates with periodically modulated scattering length, revealing new instability phenomena not present in homogeneous cases.

## Contribution

It provides a combined analytical and numerical study of dark soliton stability in inhomogeneous BECs, highlighting novel instability mechanisms caused by scattering length modulation.

## Key findings

- Oscillatory instability of single dark solitons due to modulation
- Absence of instabilities near the linear limit for two dark solitons
- Exponential instability in three dark solitons with in-phase motion

## Abstract

We examine the spectral properties of single and multiple matter-wave dark solitons in Bose-Einstein condensates confined in parabolic traps, where the scattering length is periodically modulated. In addition to the large-density limit picture previously established for homogeneous nonlinearities, we explore a perturbative analysis in the vicinity of the linear limit, which provides good agreement with the observed spectral modes. Between these two analytically tractable limits, we use numerical computations to fill in the relevant intermediate regime. We find that the scattering length modulation can cause a variety of features absent for homogeneous nonlinearities. Among them, we note the potential oscillatory instability even of the single dark soliton, the potential absence of instabilities in the immediate vicinity of the linear limit for two dark solitons, and the existence of an exponential instability associated with the in-phase motion of three dark solitons.