2 research outputs found
Multibreather and vortex breather stability in Klein--Gordon lattices: Equivalence between two different approaches
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 model
Stability of non-time-reversible phonobreathers
Non-time reversible phonobreathers are non-linear waves that can transport
energy in coupled oscillator chains by means of a phase-torsion mechanism. In
this paper, the stability properties of these structures have been considered.
It has been performed an analytical study for low-coupling solutions based upon
the so called {\em multibreather stability theorem} previously developed by
some of the authors [Physica D {\bf 180} 235]. A numerical analysis confirms
the analytical predictions and gives a detailed picture of the existence and
stability properties for arbitrary frequency and coupling.Comment: J. Phys. A.:Math. and Theor. In Press (2010