We present recent existence results of quasi-periodic solutions for Schrödinger equations with a multiplicative potential on T_d_, , 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 in then the solutions are in . The proofs are based on an improved Nash-Moser iterative scheme and a new multiscale inductive analysis for the inverse linearized operators.
Cite this article
Massimiliano Berti, Philippe Bolle, Quasi-periodic solutions of nonlinear Schrödinger equations on T<i><sup>d</sup></i>. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 22 (2011), no. 2, pp. 223–236DOI 10.4171/RLM/597