Metastability phenomena in two-dimensional rectangular lattices with nearest-neighbour interaction
(2021) In Nonlinearity 34(7). p.4983-5044- Abstract
We study analytically the dynamics of two-dimensional rectangular lattices with periodic boundary conditions. We consider anisotropic initial data supported on one low-frequency Fourier mode. We show that, in the continuous approximation, the resonant normal form of the system is given by integrable PDEs. We exploit the normal form in order to prove the existence of metastability phenomena for the lattices. More precisely, we show that the energy spectrum of the normal modes attains a distribution in which the energy is shared among a packet of low-frequencies modes; such distribution remains unchanged up to the time-scale of validity of the continuous approximation.
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https://lup.lub.lu.se/record/a43e6a8a-c536-46a2-92a1-8ea13d47f09f
- author
- Gallone, M. and Pasquali, S. LU
- organization
- publishing date
- 2021
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- continuous approximation, energy localization, metastability
- in
- Nonlinearity
- volume
- 34
- issue
- 7
- pages
- 62 pages
- publisher
- London Mathematical Society / IOP Science
- external identifiers
-
- scopus:85110566997
- ISSN
- 0951-7715
- DOI
- 10.1088/1361-6544/ac0483
- language
- English
- LU publication?
- yes
- id
- a43e6a8a-c536-46a2-92a1-8ea13d47f09f
- date added to LUP
- 2021-08-23 09:47:06
- date last changed
- 2022-04-27 03:20:32
@article{a43e6a8a-c536-46a2-92a1-8ea13d47f09f,
abstract = {{<p>We study analytically the dynamics of two-dimensional rectangular lattices with periodic boundary conditions. We consider anisotropic initial data supported on one low-frequency Fourier mode. We show that, in the continuous approximation, the resonant normal form of the system is given by integrable PDEs. We exploit the normal form in order to prove the existence of metastability phenomena for the lattices. More precisely, we show that the energy spectrum of the normal modes attains a distribution in which the energy is shared among a packet of low-frequencies modes; such distribution remains unchanged up to the time-scale of validity of the continuous approximation.</p>}},
author = {{Gallone, M. and Pasquali, S.}},
issn = {{0951-7715}},
keywords = {{continuous approximation; energy localization; metastability}},
language = {{eng}},
number = {{7}},
pages = {{4983--5044}},
publisher = {{London Mathematical Society / IOP Science}},
series = {{Nonlinearity}},
title = {{Metastability phenomena in two-dimensional rectangular lattices with nearest-neighbour interaction}},
url = {{http://dx.doi.org/10.1088/1361-6544/ac0483}},
doi = {{10.1088/1361-6544/ac0483}},
volume = {{34}},
year = {{2021}},
}