Blow up in finite time and dynamics of blow up solutions for the L^2-critical generalized KdV equation

In this paper, we are interested in the phenomenon of blow up in finite time (or formation of singularity in finite time) of solutions of the critical generalized KdV equation. Few results are known in the context of partial differential equations with a Hamiltonian structure. For the semilinear wave equation, or more generally for hyperbolic systems, the finite speed of propagation allows one to build blowing up solutions by reducing the problem to an ordinary differential equation. For the nonlinear Schrödinger equation, iut = −∆u− |u|p−1u, where u : R×R → C, (1)