JournalsrlmVol. 22, No. 2pp. 223–236

Quasi-periodic solutions of nonlinear Schrödinger equations on T<i><sup>d</sup></i>

  • Massimiliano Berti

    Università degli Studi di Napoli Federico II, Italy
  • Philippe Bolle

    Université d'Avignon et des Pays de Vaucluse, France
Quasi-periodic solutions of nonlinear Schrödinger equations on  T<i><sup>d</sup></i> cover

Abstract

We present recent existence results of quasi-periodic solutions for Schrödinger equations with a multiplicative potential on T_d_, d1d \geq 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 in CC^\infty then the solutions are in CC^\infty . 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. 223–236

DOI 10.4171/RLM/597