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Lattice dynamics on large time scales and dispersive effective equations
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Schweizer, Ben and Theil, Florian (2018) Lattice dynamics on large time scales and dispersive effective equations. SIAM Journal on Applied Mathematics, 78 (6). pp. 3060-3086. doi:10.1137/17M1162184 ISSN 0036-1399.
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Official URL: https://doi.org/10.1137/17M1162184
Abstract
We investigate the long time behavior of waves in crystals. Starting from a linear wave equation on a discrete lattice with periodicity $\varepsilon>0$, we derive the continuum limit equation for time scales of order $\varepsilon^{-2}$. The effective equation is a weakly dispersive wave equation of fourth order. Initial values with bounded support result in ring-like solutions, and we characterize the dispersive long time behavior of the radial profiles with a linearized KdV equation of third order.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics Q Science > QD Chemistry |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Library of Congress Subject Headings (LCSH): | Lattice dynamics , Lattice theory , Crystallography, Mathematical, Wave equation | ||||||
Journal or Publication Title: | SIAM Journal on Applied Mathematics | ||||||
Publisher: | Society for Industrial and Applied Mathematics | ||||||
ISSN: | 0036-1399 | ||||||
Official Date: | 15 November 2018 | ||||||
Dates: |
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Volume: | 78 | ||||||
Number: | 6 | ||||||
Page Range: | pp. 3060-3086 | ||||||
DOI: | 10.1137/17M1162184 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Re-use Statement: | “First Published in SIAM Journal on Applied Mathematics in 78(6)2018, published by the Society for Industrial and Applied Mathematics (SIAM)” and the copyright notice as stated in the article itself (e.g., “Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.”) | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 17 September 2018 | ||||||
Date of first compliant Open Access: | 10 January 2019 | ||||||
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