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
Contributor : Denys Dutykh
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Submitted on : Monday, February 5, 2018 - 9:59:44 AM
Last modification on : Tuesday, February 5, 2019 - 11:24:15 AM
Document(s) archivé(s) le : Wednesday, May 2, 2018 - 2:49:07 PM
