Unique continuation for discrete nonlinear wave equations
Exactly Solvable and Integrable Systems
2012-04-03 v2 Dynamical Systems
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.
Cite
@article{arxiv.0904.0011,
title = {Unique continuation for discrete nonlinear wave equations},
author = {Helge Krueger and Gerald Teschl},
journal= {arXiv preprint arXiv:0904.0011},
year = {2012}
}
Comments
10 pages