450 research outputs found
Discrete Breathers
Nonlinear classical Hamiltonian lattices exhibit generic solutions in the
form of discrete breathers. These solutions are time-periodic and (typically
exponentially) localized in space. The lattices exhibit discrete translational
symmetry. Discrete breathers are not confined to certain lattice dimensions.
Necessary ingredients for their occurence are the existence of upper bounds on
the phonon spectrum (of small fluctuations around the groundstate) of the
system as well as the nonlinearity in the differential equations. We will
present existence proofs, formulate necessary existence conditions, and discuss
structural stability of discrete breathers. The following results will be also
discussed: the creation of breathers through tangent bifurcation of band edge
plane waves; dynamical stability; details of the spatial decay; numerical
methods of obtaining breathers; interaction of breathers with phonons and
electrons; movability; influence of the lattice dimension on discrete breather
properties; quantum lattices - quantum breathers. Finally we will formulate a
new conceptual aproach capable of predicting whether discrete breather exist
for a given system or not, without actually solving for the breather. We
discuss potential applications in lattice dynamics of solids (especially
molecular crystals), selective bond excitations in large molecules, dynamical
properties of coupled arrays of Josephson junctions, and localization of
electromagnetic waves in photonic crystals with nonlinear response.Comment: 62 pages, LaTeX, 14 ps figures. Physics Reports, to be published; see
also at http://www.mpipks-dresden.mpg.de/~flach/html/preprints.htm
Nonlinear guided waves and spatial solitons in a periodic layered medium
We overview the properties of nonlinear guided waves and (bright and dark)
spatial optical solitons in a periodic medium created by a sequence of linear
and nonlinear layers. First, we consider a single layer with a cubic nonlinear
response (a nonlinear waveguide) embedded into a periodic layered linear
medium, and describe nonlinear localized modes (guided waves and Bragg-like
localized gap modes) and their stability. Then, we study modulational
instability as well as the existence and stability of discrete spatial solitons
in a periodic array of identical nonlinear layers, a one-dimensional nonlinear
photonic crystal. Both similarities and differences with the models described
by the discrete nonlinear Schrodinger equation (derived in the tight-binding
approximation) and coupled-mode theory (valid for the shallow periodic
modulations) are emphasized.Comment: 10 pages, 14 figure
A discrete nonlinear model with substrate feedback
We consider a prototypical model in which a nonlinear field (continuum or
discrete) evolves on a flexible substrate which feeds back to the evolution of
the main field. We identify the underlying physics and potential applications
of such a model and examine its simplest one-dimensional Hamiltonian form,
which turns out to be a modified Frenkel-Kontorova model coupled to an extra
linear equation. We find static kink solutions and study their stability, and
then examine moving kinks (the continuum limit of the model is studied too). We
observe how the substrate effectively renormalizes properties of the kinks. In
particular, a nontrivial finding is that branches of stable and unstable kink
solutions may be extended beyond a critical point at which an effective
intersite coupling vanishes; passing this critical point does not destabilize
the kink. Kink-antikink collisions are also studied, demonstrating alternation
between merger and transmission cases.Comment: a revtex text file and 6 ps files with figures. Physical Review E, in
pres
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