An extension of KAM theory to quasi-periodic breather solutions in Hamiltonian lattice systems
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.
Advisor:Weiss, Howard; Bellissard, Jean; Yi, Yingfei; Dieci, Luca; Verriest, Erik I.
School:Georgia Institute of Technology
School Location:USA - Georgia
Source Type:Master's Thesis
Date of Publication:11/14/2007