Self similar finite energy solutions to the supercritical generalized Korteweg-de-Vries equation

There is strong evidence of asymptotically self similar blow up for the super critical nonlinear Schroedinger equation and the related Korteweg-de-Vries equation. Recently Merle, Raphael and Szeftel studied the blow-up dynamics for the slightly supercritical nonlinear Schrödinger equation.

In this talk I will present a bifurcation analysis for the bifurcation of self similar finite energy solutions from the travelling wave solution for the focussing generalized Korteweg-de-Vries equation. The difficulty comes from a rich family of asymptotic regimes, which have to be understood and controlled simultaneously.