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A note on the construction of Sobolev almost periodic invariant tori for the 1d NLS. (English) Zbl 1473.37091

Summary: 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.

MSC:

37K55 Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems
35B15 Almost and pseudo-almost periodic solutions to PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)
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