On the existence of quasi-periodic lattice oscillations
Classical Analysis and ODEs
2007-05-23 v1 Mathematical Physics
Dynamical Systems
math.MP
Abstract
We construct multi-phase travelling waves which are periodic in time and quasi-periodic in the spatial variable for infinite nonlinear chains with nearest neighbor interactions. The main difficulty in the construction is a small divisor problem. We prove a KAM-type theorem for an infinite dimensional system following the approach of W. Craig and C. E Wayne which was further developed by J. Bourgain.
Keywords
Cite
@article{arxiv.math/0502077,
title = {On the existence of quasi-periodic lattice oscillations},
author = {Thomas Kriecherbauer},
journal= {arXiv preprint arXiv:math/0502077},
year = {2007}
}
Comments
160 pages