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 <>
Soumis le : lundi 26 juin 2017 - 20:21:56
Dernière modification le : vendredi 7 juillet 2017 - 01:05:15
Denys Dutykh, Jean-Guy Caputo. Wave dynamics on networks: method and application to the sine-Gordon equation. 30 pages, 9 figures, 2 tables, 36 references. Other author's papers can be downloaded at http://w.. 2015. <hal-01160840v2>
