Shock wave occurrence and soliton propagation in polariton condensates

Abstract

We study the effects of the gain and the loss of polaritons on the wave propagation in polariton condensates. This system is described by a modified Gross–Pitaevskii equation. In the case of small damping, we use the reductive perturbation method to transform this equation; we get a modified Burgers equation in the dispersionless limit and a damped Korteweg – de Vries equation in a more general case. We demonstrate that the shock wave occurrence depends on the gain and the loss of polaritons in the dispersionless polariton condensate. The resolution of the damped Korteweg – de Vries equation shows that the soliton behaves like a damped wave in the case of a constant damping. Based on an asymptotic solution, the survival time and the distance traveled by this soliton are evaluated. We solve the damped Korteweg – de Vries equation and the modified Gross–Pitaevskii numerically to validate the analytical calculations and discuss especially the soliton propagation in the system.