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.

An extensive resonant normal form for an arbitrary large Klein-Gordon model / S. Paleari, T. Penati. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 1618-1891. - 195:1(2016 Feb), pp. 133-165. [10.1007/s10231-014-0456-9]

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

S. Paleari
Primo
;
T. Penati
2016

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.
Extensivity; Resonant normal form; Klein–Gordon model; Anticontinuum limit; Thermodynamic limit; Generalized dNLS model
Settore MAT/07 - Fisica Matematica
Teorie geometriche e analitiche dei sistemi Hamiltoniani in dimensioni finite e infinite
15-ott-2014
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/252572
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