Cavitation induced by explosion in an ideal fluid model

Wave instabilities in the presence of non vanishing background in nonlinear Schrödinger systems

We investigate wave collapse ruled by the generalized nonlinear Schrödinger (NLS) equation in 1+1 dimensions, for localized excitations with non-zero background, establishing through virial identities a new criterion for blow-up. When collapse is arrested, a semiclassical approach allows us to show that the system can favor the formation of dispersive shock waves. The general findings are illustrated with a model of interest to both classical and quantum physics (cubic-quintic NLS equation), demonstrating a radically novel scenario of instability, where solitons identify a marginal condition between blow-up and occurrence of shock waves, triggered by arbitrarily small mass perturbations of different sign.

Coherent cavitation in the liquid of light

We study the cubic- (focusing-)quintic (defocusing) nonlinear Schrödinger equation in two transverse dimensions. We discuss a family of stationary traveling waves, including rarefaction pulses and vortex-antivortex pairs, in a background of critical amplitude. We show that these rarefaction pulses can be generated inside a flattop soliton when a smaller bright soliton collides with it. The fate of the evolution strongly depends on the relative phase of the solitons. Among several possibilities, we find that the dark pulse can reemerge as a bright soliton.