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

  • Joachim Krieger

    EPFL, Lausanne, Switzerland
  • Wilhelm Schlag

    University of Chicago, United States

Abstract

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.

Cite this article

Joachim Krieger, Wilhelm Schlag, Non-generic blow-up solutions for the critical focusing NLS in 1-D. J. Eur. Math. Soc. 11 (2009), no. 1, pp. 1–125

DOI 10.4171/JEMS/143