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

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

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,...

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Veröffentlicht in:Advances in Mathematical Physics 2018-01, Vol.2018 (2018), p.1-12
1. Verfasser: Christov, Ognyan
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Dynamical systems
Equilibrium
Integrals
Lattice theory
Lattices
Mechanics
Neighborhoods
Symmetry
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Zusammenfassung: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.
ISSN:1687-9120
1687-9139
DOI:10.1155/2018/7023696