Abstract
We construct the “threshold manifold” near the soliton for the mass critical gKdV equation, completing results obtained in Martel et al. (Acta Math 212:59–140, 2014, J Math Eur Soc 2015). In a neighborhood of the soliton, this C 1 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.
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Martel, Y., Merle, F., Nakanishi, K. et al. Codimension One Threshold Manifold for the Critical gKdV Equation. Commun. Math. Phys. 342, 1075–1106 (2016). https://doi.org/10.1007/s00220-015-2509-3
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DOI: https://doi.org/10.1007/s00220-015-2509-3