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.
https://hal.archives-ouvertes.fr/hal-01160840
Contributeur : Denys Dutykh
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Soumis le : lundi 5 février 2018 - 09:59:44
Dernière modification le : samedi 27 octobre 2018 - 01:22:48
Document(s) archivé(s) le : mercredi 2 mai 2018 - 14:49:07
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〉
