Unique continuation for discrete nonlinear wave equations

Unique continuation for discrete nonlinear wave equations

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,...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society Vol. 140; no. 4; pp. 1321 - 1330
Main Authors: KRÜGER, HELGE, TESCHL, GERALD
Format: Journal Article
Language:English
Published: American Mathematical Society 01-04-2012
Subjects:
College mathematics
Equations
Mathematical inequalities
Mathematical lattices
Mathematical models
Wave equations
Toda lattice
discrete nonlinear Schrödinger equation
Kac-van Moerbeke lattice
Ablowitz-Ladik equations
Schur flow
Unique continuation
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Summary: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-2011-10980-8