Dark solitons near potential and nonlinearity steps

TL;DR

This paper develops a particle-based theoretical framework to analyze dark soliton behavior near potential and nonlinearity steps, applicable to Bose-Einstein condensates and nonlinear optics, with predictions validated by numerical simulations.

Contribution

It introduces an effective particle theory for dark solitons near steps, providing analytical insights into their static and dynamic behavior in complex potential landscapes.

Findings

Analytical predictions match numerical results closely.

The theory describes reflection, transmission, and trapping of solitons at steps.

Extension to multiple steps and barrier potentials is discussed.

Abstract

We study dark solitons near potential and nonlinearity steps and combinations thereof, forming rectangular barriers. This setting is relevant to the contexts of atomic Bose-Einstein condensates (where such steps can be realized by using proper external fields) and nonlinear optics (for beam propagation near interfaces separating optical media of different refractive indices). We use perturbation theory to develop an equivalent particle theory, describing the matter-wave or optical soliton dynamics as the motion of a particle in an effective potential. This Newtonian dynamical problem provides information for the soliton statics and dynamics, including scenarios of reflection, transmission, or quasi-trapping at such steps. The case of multiple such steps and its connection to barrier potentials is also touched upon. Our analytical predictions are found to be in very good agreement with the corresponding numerical results.