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The dynamics of unstable waves
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Law, K. J. H. and Hoq, Q. Enam (2009) The dynamics of unstable waves. In: Kevrekidis, Panayotis G., (ed.) The Discrete Nonlinear Schrödinger Equation :Discretized equations in which the evolution variable is continuous while the spatial variables are confined to the points on a lattice, have had a significant presence and impact across multiple disciplines [1. Springer, pp. 205-220. ISBN 9783540891987
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Official URL: http://dx.doi.org/10.1007/978-3-540-89199-4_10
Abstract
Discretized equations in which the evolution variable is continuous while the spatial variables are confined to the points on a lattice, have had a significant presence and impact across multiple disciplines [1–6]. This should not be surprising considering that many natural processes and phenomena exhibit discrete structure [7–11]. As particular examples, we see that in physics the discrete nonlinear Schrödinger equation was used to model periodic optical structures [12], while in biology the Davydov equations model energy transfer in proteins [13]. These diverse phenomena are testament to the ubiquitousness of discrete regimes across diverse settings, and hence validate the need to study them. The study of discretized equations can be traced at least back to the work of Frenkel and Kontorova on crystal dislocations [14] and the Fermi–Pasta–Ulam problem [15].
| Item Type: | Book Item | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Science > Mathematics | ||||
| Publisher: | Springer | ||||
| ISBN: | 9783540891987 | ||||
| ISSN: | 0081-3869 | ||||
| Book Title: | The Discrete Nonlinear Schrödinger Equation :Discretized equations in which the evolution variable is continuous while the spatial variables are confined to the points on a lattice, have had a significant presence and impact across multiple disciplines [1 | ||||
| Editor: | Kevrekidis, Panayotis G. | ||||
| Official Date: | 2009 | ||||
| Dates: |
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| Volume: | Vol.232 | ||||
| Number of Pages: | 416 | ||||
| Page Range: | pp. 205-220 | ||||
| DOI: | 10.1007/978-3-540-89199-4_10 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published |
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