Focusing singularity in a derivative nonlinear Schrodinger equation

We present a numerical study of a derivative nonlinear Schrodinger equation with a general power nonlinearity, vertical bar psi vertical bar(2 sigma) psi(x). In the L-2-supercritical regime, sigma > 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 Schrodinger equation with supercritical power law nonlinearity. (C) 2013 Elsevier B.V. All rights reserved.