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An extensive resonant normal form for an arbitrary large Klein–Gordon model

2014/04/30 by Simone Paleari, Tiziano Penati · 1 citation
Mathematics · Physics and Astronomy · #Boundary (topology) #Boundary value problem #Coupling (piping) #Limit (mathematics) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Normal mode #Order (exchange) #Quantum Mechanics and Non-Hermitian Physics #math.DS

paper · pdf · doi:10.1007/s10231-014-0456-9

Substantial revision in the presentation. Corrected and estimate in Corollary 3.1. To appear in Annali di Matematica Pura e Applicata

arxiv created 2014/10/08 · openalex publication_date 2014/10/15 · arxiv updated 2014/12/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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.

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