ON ALMOST PERIODIC SOLUTIONS TO NLS WITHOUT EXTERNAL PARAMETERS

The paper proves, for every real-entire nonlinearity f with f(0)=0, f′(0)≠0 and mild growth, the existence of nonresonant infinite-dimensional Kronecker tori (equivalently: almost periodic solutions) for the 1D periodic NLS, via a regularizing normal form and a KAM scheme with internal parameters; this is stated in Definition 1.1 and Theorem 1.2 and sketched across Sections 2–3 of the note . The model’s solution constructs such a torus for the integrable defocusing cubic NLS by global Birkhoff coordinates and a Baire-type nonresonance selection, which indeed yields a valid example within the paper’s hypothesis class (it picks f(ρ)=2ρ). Hence both are correct, but the paper establishes a much stronger, nonintegrable, parameter-free result, while the model solves only a special integrable case and (now outdatedly) remarks that the general case is open.