A Korteweg-de Vries description of dark solitons in polariton superfluids

TL;DR

This paper models dark soliton dynamics in polariton superfluids using a Korteweg-de Vries equation derived from a generalized open-dissipative Gross-Pitaevskii framework, revealing decay and shelf phenomena.

Contribution

It introduces a novel analytical approach linking dark soliton behavior in polariton condensates to a KdV equation with dissipation, expanding understanding of soliton decay and shelf formation.

Findings

Dark solitons decay with a rate analytically derived in weak pumping.

A shelf forms during soliton evolution, consistent with the KdV model.

The model accurately describes soliton dynamics in the studied regime.

Abstract

We study the dynamics of dark solitons in an incoherently pumped exciton-polariton condensate by means of a system composed by a generalized open-dissipative Gross-Pitaevskii equation for the polaritons' wavefunction and a rate equation for the exciton reservoir density. Considering a perturbative regime of sufficiently small reservoir excitations, we use the reductive perturbation method, to reduce the system to a Korteweg-de Vries (KdV) equation with linear loss. This model is used to describe the analytical form and the dynamics of dark solitons. We show that the polariton field supports decaying dark soliton solutions with a decay rate determined analytically in the weak pumping regime. We also find that the dark soliton evolution is accompanied by a shelf, whose dynamics follows qualitatively the effective KdV picture.