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arXiv · 1006.0346

Multibreather and vortex breather stability in Klein--Gordon lattices: Equivalence between two different approaches

J. Cuevas·V. Koukouloyannis·P. G. Kevrekidis·J. F. R. Archilla
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Abstract

In this work, we revisit the question of stability of multibreather configurations, i.e., discrete breathers with multiple excited sites at the anti-continuum limit of uncoupled oscillators. We present two methods that yield quantitative predictions about the Floquet multipliers of the linear stability analysis around such exponentially localized in space, time-periodic orbits, based on the Aubry band method and the MacKay effective Hamiltonian method and prove that their conclusions are equivalent. Subsequently, we showcase the usefulness of the methods by a series of case examples including one-dimensional multi-breathers, and two-dimensional vortex breathers in the case of a lattice of linearly coupled oscillators with the Morse potential and in that of the discrete $ϕ^4$ model.

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J. Cuevas, V. Koukouloyannis, P. G. Kevrekidis, J. F. R. Archilla. 2010-06-02. Multibreather and vortex breather stability in Klein--Gordon lattices: Equivalence between two different approaches. https://doi.org/10.1142/s0218127411029690

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