Non-radial implosion for the defocusing nonlinear Schrödinger equation in ${\mathbb{T}}^d$ and ${\mathbb{R}}^d$

Abstract

In this paper we construct smooth, non-radial solutions of the defocusing nonlinear Schrödinger equation that develop an imploding finite time singularity, both in the periodic setting and the full space.

44 pages, 5 figures