Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1898430 | Physica D: Nonlinear Phenomena | 2013 | 11 Pages |
•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.