Unique continuation for discrete nonlinear wave equations

Details Unique continuation for discrete nonlinear wave equations Unique continuation for discrete nonlinear wave equations

2009-03-31

arxiv.org/abs/0904.0011v2

Proc. Amer. Math. Soc. 140, 1321-1330 (2012)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

10 pages

Scientific paper

10.1090/S0002-9939-2011-10980-8

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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