%0 Journal Article
%T On the existence of quasi-periodic lattice oscillations
%A Thomas Kriecherbauer
%J Mathematics
%D 2005
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/0502077v1