Periodic solutions of nonlinear Schrödinger equations: a paradifferential approach

Delort, Jean-Marc

doi:10.2140/apde.2011.4.639

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Periodic solutions of nonlinear Schrödinger equations: a paradifferential approach

Jean-Marc Delort

Vol. 4 (2011), No. 5, 639–676

DOI: 10.2140/apde.2011.4.639

Abstract

This paper is devoted to the construction of periodic solutions of nonlinear Schrödinger equations on the torus, for a large set of frequencies. Usual proofs of such results rely on the use of Nash–Moser methods. Our approach avoids this, exploiting the possibility of reducing, through paradifferential conjugation, the equation under study to an equivalent form for which periodic solutions may be constructed by a classical iteration scheme.

Keywords

nonlinear Schrödinger equation, periodic solutions

Mathematical Subject Classification 2000

Primary: 35B10, 35Q55

Milestones

Received: 16 October 2009

Revised: 13 January 2010

Accepted: 14 September 2010

Published: 16 February 2012

Proposed: Maciej Zworski

Authors

Jean-Marc Delort
Université Paris 13, Institut Galilée CNRS, UMR 7539, Laboratoire Analyse Géométrie et Applications 99, Avenue J.-B. Clément F-93430 Villetaneuse France

Vol. 4, No. 5, 2011