Existence and non-existence of localised solutions in damped and driven general nonlinear lattices

Date

Apr 8, 2014

Time

11:00 AM - 12:00 PM

Speaker

Dirk Hennig

Language

en

Main Topic

Physik

Other Topics

Physik

Host

Colm Mulhern

Description

The existence of spatially localised solutions, in the form of discrete breathers, in general damped and driven nonlinear lattice systems of coupled oscillators is investigated. Conditions for the exponential decay of the difference between the maximal and minimal amplitudes of the oscillators are provided which proves that initial non- uniform spatial patterns representing breathers attain exponentially fast a spatially uniform state preventing the formation and/or preservation of any breather solution at all. Strikingly the results are generic in the sense that they hold for arbitrary dimension of the system, any attractive interaction, coupling strength and on-site potential and general driving fields. Furthermore, the rigorous quantitative results establish conditions under which discrete breathers in general damped and driven nonlinear lattices can exist at all and open the way for further research on the emergent dynamical scenarios, in particular features of pattern formation, localisation and synchronisation, in coupled cell networks.

Last modified: Apr 8, 2014, 10:03:00 AM