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Quasi-periodic solutions with Sobolev regularity of NLS on 𝕋 d with a multiplicative potential

Massimiliano Berti, Philippe Bolle (2013)

Journal of the European Mathematical Society

We prove the existence of quasi-periodic solutions for Schrödinger equations with a multiplicative potential on 𝕋 d , d 1 , finitely differentiable nonlinearities, and tangential frequencies constrained along a pre-assigned direction. The solutions have only Sobolev regularity both in time and space. If the nonlinearity and the potential are C then the solutions are C . The proofs are based on an improved Nash-Moser iterative scheme, which assumes the weakest tame estimates for the inverse linearized operators...

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