On the existence of quasi-periodic lattice oscillations

Details On the existence of quasi-periodic lattice oscillations On the existence of quasi-periodic lattice oscillations

2005-02-03

arxiv.org/abs/math/0502077v1

Mathematics

Classical Analysis and ODEs

160 pages

Scientific paper

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.

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