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

TL;DR

This paper provides numerical evidence of a new type of highly oscillatory singularity forming in defocusing fractional nonlinear Schrödinger equations with small, energy supercritical fractional powers, expanding understanding of singularity formation in such dispersive systems.

Contribution

It introduces numerical evidence for a novel highly oscillatory singularity in defocusing fractional NLS with small fractional powers, a case previously unexplored.

Findings

Evidence of highly oscillatory singularity formation

Singularity occurs in energy supercritical regime

Numerical simulations support theoretical predictions

Abstract

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.