Soliton excitations in a polariton condensate with defects

Abstract

To study soliton excitations in a polariton condensate with defects, we use the Gross–Pitaevskii equation and its hydrodynamic form. An extra term is added to take into account the non-equilibrium nature of the polariton condensate and the presence of defects. The reductive perturbation method transforms these hydrodynamic equations into a modified Korteweg–de Vries equation in the long wavelength limit. We linearize this equation and study the soliton linear excitations. We give an analytic expression of traveling excitations using the variation of constants method. In the more general form, we show numerically that the excitations are oscillations, i.e., the amplitude and the width of the dark soliton oscillate simultaneously but in an opposite way.