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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Unique continuation for discrete nonlinear wave equations
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by Helge Krüger and Gerald Teschl PDF
Proc. Amer. Math. Soc. 140 (2012), 1321-1330 Request permission

Abstract:

We establish unique continuation for various discrete nonlinear wave equations. For example, we show that if two solutions of the Toda lattice coincide for one lattice point in some arbitrarily small time interval, then they coincide everywhere. Moreover, we establish analogous results for the Toda, Kac–van Moerbeke, and Ablowitz–Ladik hierarchies. Although all these equations are integrable, the proof does not use integrability and can be adapted to other equations as well.
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Additional Information
  • Helge Krüger
  • Affiliation: Department of Mathematics, Rice University, Houston, Texas 77005
  • Address at time of publication: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
  • Email: helge@caltech.edu
  • Gerald Teschl
  • Affiliation: Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, 1090 Wien, Austria — and — International Erwin Schrödinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Wien, Austria
  • Email: Gerald.Teschl@univie.ac.at
  • Received by editor(s): April 1, 2009
  • Received by editor(s) in revised form: December 30, 2010
  • Published electronically: August 1, 2011
  • Additional Notes: Research supported by the Austrian Science Fund (FWF) under grant No. Y330 and the National Science Foundation (NSF) under grant No. DMS–0800100.
  • Communicated by: Walter Van Assche
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 1321-1330
  • MSC (2010): Primary 35L05, 37K60; Secondary 37K15, 37K10
  • DOI: https://doi.org/10.1090/S0002-9939-2011-10980-8
  • MathSciNet review: 2869115