Chiral solitons in a quantum potential

We study chiral solitons in a quantum potential using a dimensional reduction of the problem for $(2+1)$-dimensional anyons. We show that the integrable version of the model is described by a family of the resonant derivative nonlinear Schrödinger equations. For a quantum potential strength $s>1$, we show that the chiral soliton interaction has a resonance. We investigate the semiclassical quantization procedure for solitons.