An extension of KAM theory to quasi-periodic breather solutions in Hamiltonian lattice systems

KAM theory;Hamiltonian;Lattice;Quasi-periodic breathers

Viveros Rogel, Jorge ; Mathematics

University:Georgia Institute of Technology

Department:Mathematics

关键词: KAM theory;    Hamiltonian;    Lattice;    Quasi-periodic breathers;   

Others  :  https://smartech.gatech.edu/bitstream/1853/19869/1/viveros_jorge_200712_phd.pdf

美国|英语

来源: SMARTech Repository

【 摘 要 】

We prove the existence and linear stability of quasi-periodic breather solutions in a 1d Hamiltonian lattice of identical, weakly-coupled, anharmonic oscillators with general on-site potentials and under the effect of long-ranged interaction, via de KAM technique. We prove the persistence of finite-dimensional tori which correspond in the uncoupled limit to N arbitrary lattice sites initially excited. The frequencies of the invariant tori of the perturbed system are only slightly deformed from the frequencies of the unperturbed tori.