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      Multi-site breathers in Klein-Gordon lattices: stability, resonances, and bifurcations

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          Abstract

          We prove the most general theorem about spectral stability of multi-site breathers in the discrete Klein-Gordon equation with a small coupling constant. In the anti-continuum limit, multi-site breathers represent excited oscillations at different sites of the lattice separated by a number of "holes" (sites at rest). The theorem describes how the stability or instability of a multi-site breather depends on the phase difference and distance between the excited oscillators. Previously, only multi-site breathers with adjacent excited sites were considered within the first-order perturbation theory. We show that the stability of multi-site breathers with one-site holes change for large-amplitude oscillations in soft nonlinear potentials. We also discover and study a symmetry-breaking (pitchfork) bifurcation of one-site and multi-site breathers in soft quartic potentials near the points of 1:3 resonance.

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          Most cited references10

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          Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators

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            On Explicit Recursive Formulas in the Spectral Perturbation Analysis of a Jordan Block

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              Normal-internal resonances in quasi-periodically forced oscillators: a conservative approach

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                Author and article information

                Journal
                2011-11-10
                2013-01-12
                Article
                10.1088/0951-7715/25/12/3423
                1111.2557
                caba5b0b-6ba7-4238-9bcb-7b559a53cb08

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                Nonlinearity 25 (2012) 3423-3451
                34 pages, 12 figures
                nlin.PS math-ph math.MP

                Mathematical physics,Mathematical & Computational physics,Nonlinear & Complex systems

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