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Advances in Mathematical Physics
Volume 2018 (2018), Article ID 7023696, 12 pages
https://doi.org/10.1155/2018/7023696
Research Article

Near-Integrability of Low-Dimensional Periodic Klein-Gordon Lattices

Faculty of Mathematics and Informatics, Sofia University, 5 J. Bourchier Blvd., 1164 Sofia, Bulgaria

Correspondence should be addressed to Ognyan Christov; gb.aifos-inu.imf@votsirhc

Received 30 September 2017; Accepted 24 December 2017; Published 22 January 2018

Academic Editor: Alkesh Punjabi

Copyright © 2018 Ognyan Christov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The low-dimensional periodic Klein-Gordon lattices are studied for integrability. We prove that the periodic lattice with two particles and certain nonlinear potential is nonintegrable. However, in the cases of up to six particles, we prove that their Birkhoff-Gustavson normal forms are integrable, which allows us to apply KAM theory in most cases.