2010/06/02 by J. Cuevas, J. CUEVAS, V. Koukouloyannis +3 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Breather #Classical mechanics #Eigenvalues and eigenvectors #Floquet theory #Hamiltonian (control theory) #Lattice (music) #Linear stability #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Nonlinear system #Physics #Quantum mechanics #Stability (learning theory) #Strong Light-Matter Interactions #Vortex #nlin.PS
paper · pdf · doi:10.1142/s0218127411029690
published as Int. J. Bifurcation Chaos 21, 2161 (2011)
arxiv created 2010/06/02 · openalex publication_date 2011/07/08 · arxiv updated 2015/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 by making the suitable assumptions about the form of the bands in the Aubry band theory, their conclusions are equivalent. Subsequently, we showcase the usefulness of the methods through 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.