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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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An explicit formula for the cubic Szegő equation
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by Patrick Gérard and Sandrine Grellier PDF
Trans. Amer. Math. Soc. 367 (2015), 2979-2995 Request permission

Abstract:

We derive an explicit formula for the general solution of the cubic Szegő equation and of the evolution equation of the corresponding hierarchy. As an application, we prove that all the solutions corresponding to finite rank Hankel operators are quasiperiodic.
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Additional Information
  • Patrick Gérard
  • Affiliation: Université Paris-Sud XI, Laboratoire de Mathématiques d’Orsay, CNRS, UMR 8628, 91405 Orsay Cedex, France and Institut Universitaire de France
  • Email: Patrick.Gerard@math.u-psud.fr
  • Sandrine Grellier
  • Affiliation: Fédération Denis Poisson, MAPMO-UMR 6628, Département de Mathématiques, Université d’Orleans, 45067 Orléans Cedex 2, France
  • Email: Sandrine.Grellier@univ-orleans.fr
  • Received by editor(s): June 19, 2013
  • Received by editor(s) in revised form: October 6, 2013
  • Published electronically: September 5, 2014
  • Additional Notes: Part of this work was completed while the authors were visiting CIRM in Luminy. They are grateful to this institution for its warm hospitality
  • © Copyright 2014 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 367 (2015), 2979-2995
  • MSC (2010): Primary 37K15; Secondary 47B35
  • DOI: https://doi.org/10.1090/S0002-9947-2014-06310-1
  • MathSciNet review: 3301889