Focusing singularity in a derivative nonlinear Schrödinger equation

• This is a numerical study of a generalized derivative nonlinear Schrödinger equation.
• We observe singularity formation in the L2L2-supercritical regime.
• We obtain a precise description of the local structure of singular solutions.
• The singularity is described in terms of the blowup rate and the asymptotic profile.

We present a numerical study of a derivative nonlinear Schrödinger equation with a general power nonlinearity, |ψ|2σψx|ψ|2σψx. In the L2L2-supercritical regime, σ>1σ>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.