Non-generic blow-up solutions for the critical focusing NLS in 1-D
We consider the L-2-critical focusing non-linear Schrodinger equation in 1 + 1d. 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.
Keywords: Non-linear Schrodinger equations ; L-2-critical NLS ; pseudo-conformal blow-up ; Nonlinear Schrodinger-Equations ; Nonintegrable Equations ; Ground-States ; Stability ; Potentials ; Scattering ; Time
Record created on 2010-11-19, modified on 2016-08-08