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

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

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Cited by in corpus (4)

• Approximation of small-amplitude weakly coupled oscillators with discrete nonlinear Schrodinger equations
• On the nonexistence of degenerate phase-shift discrete solitons in a dNLS nonlocal lattice
• Collapse dynamics for the discrete nonlinear Schrödinger equation with gain and loss
• Continuation of spatially localized periodic solutions in discrete NLS lattices via normal forms