Quantization of Benjamin-Ono Solitons and Dispersive Shock Waves

ITS Seminar with Alexander Moll (Northeastern University)

A wide variety of fluid interfaces in two spatial dimensions are well-described by the Benjamin-Ono equation in the asymptotic regime of long wavelength and weak non-linearity.  In this talk, we present exact results on the quantization of Benjamin-Ono multi-phase solutions, the periodic analogs of multi-solitons, and asymptotic results for the quantization of dispersive shock waves.  In particular, we show that the semi-classical soliton spectrum is exact after the renormalization of Abanov-Wiegmann (2006) and that in the semi-classical h->0 and small dispersion e->0 limit, quantum dispersive shock waves emitted by a coherent state have microscopic wavespeeds that exhibit random matrix theory statistics for any \beta>0 where \beta/2 = e^2/h.