Proceedings of the Conference on Nonlinear Coherent Structures in Physics and Biology,
Heriot-Watt University, Edinburgh, July 95

Existence and Properties Of Discrete Breathers

S. Flach

Max-Planck-Institute for Physics of Complex Systems,
Bayreuther Str. 40 H.16, D-01187 Dresden. Germany


Nonlinear classical Hamiltonian lattices exhibit generic solutions in the form of discrete breathers. These solutions are time-periodic and (at least) exponentially localized in space. The lattices exhibit discrete translational symmetry. Discrete breathers are not confined to certain lattice dimensions. Necessary ingridients for their occurence are the existence of upper bounds on the linear spectrum (of small fluctuations around the groundstate) of the system as well as the nonlinearity. I will present existence proofs, formulate necessary existence conditions, and discuss structural stability of discrete breathers. The following results will be also discussed: the birth of breathers through tangential 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.

Conference paper.


Last modified Mon Apr 8 16:24:54 GB-Eire 1996 (DBD)