Codimension one threshold manifold for the critical gKdV equation

Abstract

We construct the 'threshold manifold' near the soliton for the mass critical gKdV equation, completing results obtained in arXiv:1204.4625 and arXiv:1204.4624. In a neighborhood of the soliton, this C1 manifold of codimension one separates solutions blowing up in finite time and solutions in the 'exit regime'. On the manifold, solutions are global in time and converge locally to a soliton. In particular, the soliton behavior is strongly unstable by blowup.

References in corpus (1)

• Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrodinger equation in the radial case

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