English

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.

Keywords

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

R2 v1 2026-06-22T03:47:43.017Z