Numerical evidence for singularity formation in defocusing fractional
NLS in one space dimension
Numerical evidence for singularity formation in defocusing fractional
NLS in one space dimension
We consider nonlinear dispersive equations of Schr\"odinger-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.