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Generation of dispersion in nondispersive nonlinear waves in thermal equilibrium
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Lee, Wonjung, Kovacic, G. and Cai, D. (2013) Generation of dispersion in nondispersive nonlinear waves in thermal equilibrium. Proceedings of the National Academy of Sciences of the United States of America, Volume 110 (Number 9). pp. 3237-3241. doi:10.1073/pnas.1215325110 ISSN 0027-8424.
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Official URL: http://dx.doi.org/10.1073/pnas.1215325110
Abstract
In this work, we examine the important theoretical question of whether dispersion relations can arise from purely nonlinear interactions among waves that possess no linear dispersive characteristics. Using two prototypical examples of nondispersive waves, we demonstrate how nonlinear interactions can indeed give rise to effective dispersive-wave–like characteristics in thermal equilibrium. Physically, these example systems correspond to the strong nonlinear coupling limit in the theory of wave turbulence. We derive the form of the corresponding dispersion relation, which describes the effective dispersive structures, using the generalized Langevin equations obtained in the Zwanzig–Mori projection framework. We confirm the validity of this effective dispersion relation in our numerical study using the wavenumber–frequency spectral analysis. Our work may provide insight into an important connection between highly nonlinear turbulent wave systems, possibly with no discernible dispersive properties, and the dispersive nature of the corresponding renormalized waves.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Proceedings of the National Academy of Sciences of the United States of America | ||||
Publisher: | National Academy of Sciences | ||||
ISSN: | 0027-8424 | ||||
Official Date: | 2013 | ||||
Dates: |
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Volume: | Volume 110 | ||||
Number: | Number 9 | ||||
Page Range: | pp. 3237-3241 | ||||
DOI: | 10.1073/pnas.1215325110 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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