Numerical Study of Blow-Up Mechanisms for Davey-Stewartson II Systems

We present a detailed numerical study of various blow-up issues in the context of the focusing Davey-Stewartson II equation. To this end, we study Gaussian initial data and perturbations of the lump and the explicit blow-up solution due to Ozawa. Based on the numerical results it is conjectured that the blow-up in all cases is self-similar, and that the time-dependent scaling behaves as in the Ozawa solution and not as in the stable blow-up of standard L-2 critical nonlinear Schrodinger equation. The blow-up profile is given by a dynamically rescaled lump.