Geometric finite difference schemes for the generalized hyperelastic-rod wave equation

Authors:
David Cohen;Xavier Raynaud
Affiliations:
Mathematisches Institut, Universität Basel, CH-4051 Basel, Switzerland;Center of Mathematics for Applications, University of Oslo, NO-0316 Oslo, Norway
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

Geometric integrators are presented for a class of nonlinear dispersive equations which includes the Camassa-Holm equation, the BBM equation and the hyperelastic-rod wave equation. One group of schemes is designed to preserve a global property of the equations: the conservation of energy; while the other one preserves a more local feature of the equations: the multi-symplecticity.