Numerical evidence for singularity formation in defocusing fractional NLS in one space dimension

Abstract

We consider nonlinear dispersive equations of Schrödinger-type involving fractional powers $0<s\le 1$ of the Laplacian and a defocusing power-law nonlinearity. We conduct numerical simulations in the case of small, energy supercritical $s$ and provide evidence for a novel type of highly oscillatory singularity within the solution.

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