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. PaleariPrimo
;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.
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