@article {Berti2013229,
title = {Quasi-periodic solutions with Sobolev regularity of NLS on Td with a multiplicative potential},
journal = {Journal of the European Mathematical Society},
volume = {15},
number = {1},
year = {2013},
note = {cited By (since 1996)5},
pages = {229-286},
abstract = {We prove the existence of quasi-periodic solutions for Schr{\"o}dinger equations with a multiplicative potential on Td , 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$\infty$ then the solutions are C$\infty$. The proofs are based on an improved Nash-Moser iterative scheme, which assumes the weakest tame estimates for the inverse linearized operators ("Green functions") along scales of Sobolev spaces. The key off-diagonal decay estimates of the Green functions are proved via a new multiscale inductive analysis. The main novelty concerns the measure and "complexity" estimates. {\textcopyright} European Mathematical Society 2013.},
issn = {14359855},
doi = {10.4171/JEMS/361},
author = {Massimiliano Berti and Philippe Bolle}
}