Nonlinear waves in lattice dynamical systems
by
Guillaume James
Institut de Mathématiques de Toulouse (UMR CNRS 5219), Institut National des Sciences Appliquées de Toulouse.

Nonlinear lattices (i.e. networks of interacting particles) are the object of intensive research, ranging from mathematical aspects up to complex physical issues, like understanding the thermal denaturation of DNA. The study of their dynamical properties covers a wide variety of mathematical topics, among which :

- the justification of PDE describing these systems in different scaling limits,

- the bifurcation and dynamical properties of nonlinear waves (e.g. localized pulses, shocks...),

- atomic scale oscillations and exponentially small phenomena,

- systems of coupled advance-delay differential equations,

- localized oscillations in homogeneous or heterogeneous nonlinear media.

After a brief overview of these different topics (which will be further developed in the minisymposium on lattice dynamical systems), we shall focus on the bifurcation of time-periodic localized oscillations in homogeneous and heterogeneous systems. Our approach relies on center manifold theory for infinite-dimensional maps with unbounded operators, and the analysis of nonautonomous discrete dynamical systems.

Date received: June 12, 2007

Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caum-89.