Codimension one threshold manifold for the critical gKdV equation

摘要

We construct the 'threshold manifold' near the soliton for the mass criticalgKdV equation, completing results obtained in arXiv:1204.4625 andarXiv:1204.4624. In a neighborhood of the soliton, this C1 manifold ofcodimension one separates solutions blowing up in finite time and solutions inthe 'exit regime'. On the manifold, solutions are global in time and convergelocally to a soliton. In particular, the soliton behavior is strongly unstableby blowup.