Proc. Amer. Math. Soc. 140, 1321-1330 (2012) [DOI: 10.1090/S0002-9939-2011-10980-8]

Unique continuationfor discrete nonlinear wave equations

Helge Krüger and Gerald Teschl

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.

MSC2000: Primary 35L05, 37K60; Secondary 37K15, 37K10
Keywords: Unique continuation, Toda lattice, Kac-van Moerbeke lattice, Ablowitz-Ladik equations, discrete nonlinear Schrödinger equation, Schur flow

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