Vol. 4, No. 5, 2011

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Periodic solutions of nonlinear Schrödinger equations: a paradifferential approach

Jean-Marc Delort

Vol. 4 (2011), No. 5, 639–676
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