Multiscale Problems in Three Applications - Abstract
Patz, Carsten
We study the long-time dynamics of em oscillations in lattices of infinitely many particles interacting via certain nonlinear potentials. In particular we consider the Klein-Gordon system on the infinite chain. The aim is to proof em dispersive stability of such Hamiltonian systems analogously to results known for PDEs. To do so we first recapitulate the dynamics of linear Hamiltonian systems on an infinite chain and give optimal decay rates based on the dispersion relation. Based on this we proof that if the nonlinearity is weak enough, the Klein-Gordan system shows a similar behaviour like its linearisation.