Wave dynamics on networks: method and application to the sine-Gordon equation

Abstract : We consider a scalar Hamiltonian nonlinear wave equation formulated on networks; this is a non standard problem because these domains are not locally homeomorphic to any subset of the Euclidean space. More precisely, we assume each edge to be a 1D uniform line with end points identified with graph vertices. The interface conditions at these vertices are introduced and justified using conservation laws and an homothetic argument. We present a detailed methodology based on a symplectic finite difference scheme together with a special treatment at the junctions to solve the problem and apply it to the sine-Gordon equation. Numerical results on a simple graph containing four loops show the performance of the scheme for kinks and breathers initial conditions.
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https://hal.archives-ouvertes.fr/hal-01160840
Contributeur : Denys Dutykh <>
Soumis le : lundi 5 février 2018 - 09:59:44
Dernière modification le : jeudi 19 avril 2018 - 15:14:39
Document(s) archivé(s) le : mercredi 2 mai 2018 - 14:49:07

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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 3
  • ARXIV : 1506.02405

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Denys Dutykh, Jean-Guy Caputo. Wave dynamics on networks: method and application to the sine-Gordon equation. 31 pages, 9 figures, 2 tables, 41 references. Other author's papers can be downloaded at http://w.. 2015. 〈hal-01160840v3〉

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