We consider the L2-critical focussing nonlinear 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 co-dimension one stable blow up manifold in the measurable category.
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Wilhelm Schlag, Joachim Krieger, Non-generic blow-up solutions for the critical focusing NLS in 1-D. J. Eur. Math. Soc. 11 (2009), no. 1, pp. 1–125DOI 10.4171/JEMS/143