Focusing singularity in a derivative nonlinear Schrِdinger equation

We present a numerical study of a derivative nonlinear Schrödinger equation with a general power nonlinearity, | ψ | 2 σ ψ x . In the L 2 -supercritical regime, σ > 1 , our simulations indicate that there is a finite time singularity. We obtain a precise description of the local structure of the solution in terms of the blowup rate and the asymptotic profile, in a form similar to that of the nonlinear Schrödinger equation with supercritical power law nonlinearity.