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arXiv · 1405.7841

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

Simone Paleari·Tiziano Penati
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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 Schr\"odinger 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.

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Simone Paleari, Tiziano Penati. 2014-05-30. Long time stability of small amplitude Breathers in a mixed FPU-KG model. https://arxiv.org/abs/1405.7841

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