An extensive resonant normal form for an arbitrary large Klein-Gordon model
arXiv:1404.2730 · doi:10.1007/s10231-014-0456-9
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.
Substantial revision in the presentation. Corrected and estimate in Corollary 3.1. To appear in Annali di Matematica Pura e Applicata