Non-generic blow-up solutions for the critical focusing NLS in 1-D
We consider the -critical focusing non-linear Schrödinger equation in -d. We demonstrate the existence of a large set of initial data close to the ground state soliton resulting in the pseudo-conformal type blow-up behavior. More specifically, we prove a version of a conjecture of Perelman, establishing the existence of a codimension one stable blow-up manifold in the measurable category.