Discrete sine-Gordon dynamics on networks

Abstract : In this study we consider the sine-Gordon equation formulated on domains which are not locally homeomorphic to any subset of the Euclidean space. More precisely, we formulate the discrete dynamics on trees and graphs. Each edge is assumed to be a 1D uniform lattice with end points identified with graph vertices. A special treatment is needed at the junctions in order to couple 1D lattices into a global communicating network. Our approach is based on considering the local conservation properties. Some preliminary numerical results are shown on a simple graph containing four loops. These results show the performance of the scheme in non-trivial realistic conditions.
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https://hal.archives-ouvertes.fr/hal-01160840
Contributeur : Denys Dutykh <>
Soumis le : lundi 8 juin 2015 - 10:33:05
Dernière modification le : lundi 21 mars 2016 - 17:43:50
Document(s) archivé(s) le : mardi 15 septembre 2015 - 12:06:56

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SG_Trees.pdf
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Distributed under a Creative Commons Paternité - Pas d'utilisation commerciale - Partage selon les Conditions Initiales 4.0 International License

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  • HAL Id : hal-01160840, version 1
  • ARXIV : 1506.02405

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Denys Dutykh, Jean-Guy Caputo. Discrete sine-Gordon dynamics on networks. 21 pages, 8 figures, 1 table, 20 references. Other author's papers can be downloaded at http://ww.. 2015. <hal-01160840>

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