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.
Liste complète des métadonnées

Cited literature [43 references]  Display  Hide  Download

Contributor : Denys Dutykh <>
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


Distributed under a Creative Commons Attribution - NonCommercial - ShareAlike 4.0 International License


  • HAL Id : hal-01160840, version 3
  • ARXIV : 1506.02405


Denys Dutykh, Jean-Guy Caputo. Wave dynamics on networks: method and application to the sine-Gordon equation. 2015. ⟨hal-01160840v3⟩



Record views


Files downloads