We announce a method for the construction of almost periodic solutions of the one dimensional analytic NLS with only Sobolev regularity both in time and space. This is the first result of this kind for PDEs.
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Luca Biasco, Jessica Elisa Massetti, Michela Procesi, A note on the construction of Sobolev almost periodic invariant tori for the 1d NLS. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 31 (2020), no. 4, pp. 981–993DOI 10.4171/RLM/923