Title:
An extension of KAM theory to quasi-periodic breather solutions in Hamiltonian lattice systems
An extension of KAM theory to quasi-periodic breather solutions in Hamiltonian lattice systems
Author(s)
Viveros Rogel, Jorge
Advisor(s)
Yi, Yingfei
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Abstract
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.
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Date Issued
2007-11-14
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Text
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Dissertation