Self-similar Blow-Up Profiles for Slightly Supercritical Nonlinear Schrodinger Equations

We construct radially symmetric self-similar blow-up profiles for the mass supercritical nonlinear Schrodinger equation i partial derivative(t)u + Delta u + |u|(p-1)u = 0 on R-d, close to the mass critical case and for any space dimension d >= 1. These profiles bifurcate from the ground-state solitary wave. The argument relies on the classical matched asymptotics method suggested in Sulem and Sulem (The nonlinear Schr<spacing diaeresis>odinger equation. Selffocusing and wave collapse. Applied mathematical sciences, 139, Springer, New York, 1999) which needs to be applied in a degenerate case due to the presence of exponentially small terms in the bifurcation equation related to the log-log blow-up law observed in the mass critical case.