vix.ing · top · new · best · stats · spec

Long time stability of small amplitude Breathers in a mixed FPU-KG model

2014/05/30 by Simone Paleari, Paleari, Simone, Tiziano Penati +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1405.7841

openalex publication_date 2014/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the limit of small couplings in the nearest neighbor interaction, and small total energy, we apply the resonant normal form result of a previous paper of ours to a finite but arbitrarily large mixed Fermi-Pasta-Ulam Klein-Gordon chain, i.e. with both linear and nonlinear terms in both the on-site and interaction potential, with periodic boundary conditions. An existence and orbital stability result for Breathers of such a normal form, which turns out to be a generalized discrete Nonlinear Schrödinger model with exponentially decaying all neighbor interactions, is first proved. Exploiting such a result as an intermediate step, a long time stability theorem for the true Breathers of the KG and FPU-KG models, in the anti-continuous limit, is proven.

Related