Soliton oscillations in collisionally inhomogeneous attractive Bose-Einstein condensates

TL;DR

This paper studies how spatial variations in nonlinearity affect bright matter-wave solitons in Bose-Einstein condensates, deriving their oscillation frequencies analytically and confirming with numerical simulations.

Contribution

It introduces a detailed analysis of soliton oscillations in inhomogeneous nonlinear media, combining analytical derivations with numerical validation for different condensate geometries.

Findings

Analytical expressions for soliton oscillation frequencies.

Numerical results agree well with analytical predictions.

Inhomogeneity induces a translation mode in solitons.

Abstract

We investigate bright matter-wave solitons in the presence of a spatially varying nonlinearity. It is demonstrated that a translation mode is excited due to the spatial inhomogeneity and its frequency is derived analytically and also studied numerically. Both cases of purely one-dimensional and ``cigar-shaped'' condensates are studied by means of different mean-field models, and the oscillation frequencies of the pertinent solitons are found and compared with the results obtained by the linear stability analysis.Numerical results are shown to be in very good agreement with the corresponding analytical predictions.