Breathers as metastable states for the discrete NLS equation

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2018Embargo end date: 01 Oct 2017Publisher:American Institute of Mathematical Sciences (AIMS)Journal:Discrete and Continuous Dynamical Systems, volume 38, pages 6,091-6,103 (issn: 1078-0947, eissn: 1553-5231,

Copyright policy )Funded by:NSF | Dynamical Systems Methods...

Authors: Eckmann, Jean-Pierre; Wayne, C. Eugene;

doi: 10.3934/dcds.2018136 , 10.48550/arxiv.1710.10999

arXiv: 1710.10999

Breathers as metastable states for the discrete NLS equation

- Summary
- Subjects
- Metrics

Abstract

We study metastable motions in weakly damped Hamiltonian systems. These are believed to inhibit the transport of energy through Hamiltonian, or nearly Hamiltonian, systems with many degrees of freedom. We investigate this question in a very simple model in which the breather solutions that are thought to be responsible for the metastable states can be computed perturbatively to an arbitrary order. Then, using a modulation hypothesis, we derive estimates for the rate at which the system drifts along this manifold of periodic orbits and verify the optimality of our estimates numerically.

Corrected typos. Added Acknowledgment

Related Organizations

Boston University
United States
University of Geneva
Switzerland
THE TRUSTEES OF BOSTON UNIVERSITY
United States

Keywords

breathers, FOS: Physical sciences, Ordinary lattice differential equations, Dynamical Systems (math.DS), Mathematical Physics (math-ph), Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion, metastability, normal forms, FOS: Mathematics, modulation theory, Mathematics - Dynamical Systems, Mathematical Physics

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	6
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Top 10%
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average