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

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 ${\varphi }^4$ model.

References in corpus (4)

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• Existence and spectral stability of multi-pulses in discrete Hamiltonian lattice systems
• On the nonexistence of degenerate phase-shift discrete solitons in a dNLS nonlocal lattice
• Stability of non-time-reversible phonobreathers
• Stationary multi-kinks in the discrete sine-Gordon equation
• On the continuation of degenerate periodic orbits via normal form: lower dimensional resonant tori
• Existence and non-existence of breather solutions in damped and driven nonlinear lattices
• Discrete breathers in ${\varphi }^4$ and related models
• Revisiting Multi-breathers in the discrete Klein-Gordon equation: A Spatial Dynamics Approach
• On the nonexistence of degenerate phase-shift multibreathers in a zigzag Klein-Gordon model
• Nonlinear instabilities of multi-site breathers in Klein-Gordon lattices