Unique continuation for discrete nonlinear wave equations

Krüger, Helge; Teschl, Gerald

doi:10.1090/S0002-9939-2011-10980-8

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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