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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

Unique continuation for discrete nonlinear wave equations


Authors: Helge Krüger and Gerald Teschl
Journal: Proc. Amer. Math. Soc. 140 (2012), 1321-1330
MSC (2010): Primary 35L05, 37K60; Secondary 37K15, 37K10
Published electronically: August 1, 2011
MathSciNet review: 2869115
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10980-8
Keywords: Unique continuation, Toda lattice, Kac–van Moerbeke lattice, Ablowitz–Ladik equations, discrete nonlinear Schrödinger equation, Schur flow
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
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.