We present a numerical study of a derivative nonlinear Schr\"odinger equation
with a general power nonlinearity, ∣ψ∣2σψx​. In the
L2-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 blowup rate and asymptotic profile, in a
form similar to that of the nonlinear Schr\"odinger equation with supercritical
power law nonlinearity.Comment: 24 pages, 17 figure