An extensive resonant normal form for an arbitrary large Klein-Gordon model
Dynamical Systems
2014-12-17 v2
Abstract
We consider a finite but arbitrarily large Klein-Gordon chain, with periodic boundary conditions. In the limit of small couplings in the nearest neighbor interaction, and small (total or specific) energy, a high order resonant normal form is constructed with estimates uniform in the number of degrees of freedom. In particular, the first order normal form is a generalized discrete nonlinear Schroedinger model, characterized by all-to-all sites coupling with exponentially decaying strength.
Cite
@article{arxiv.1404.2730,
title = {An extensive resonant normal form for an arbitrary large Klein-Gordon model},
author = {Simone Paleari and Tiziano Penati},
journal= {arXiv preprint arXiv:1404.2730},
year = {2014}
}
Comments
Substantial revision in the presentation. Corrected and estimate in Corollary 3.1. To appear in Annali di Matematica Pura e Applicata