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Non-generic blow-up solutions for the critical focusing NLS in 1-D

Joachim Krieger; Wilhelm Schlag — 2009

Journal of the European Mathematical Society

We consider the $L^{2}$ -critical focusing non-linear Schrödinger equation in $1 + 1$ -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.

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