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A multi-symplectic integration of the Ostrovsky equation. (English) Zbl 1271.65148

Summary: We consider structure-preserving integration of the Ostrovsky equation, which for example models gravity waves under the influence of Coriolis force. We find a multi-symplectic formulation, and derive a finite difference discretization based on the formulation and by means of the Preissman box scheme. We also present a numerical example, which shows the effectiveness of this scheme.

MSC:

65P10 Numerical methods for Hamiltonian systems including symplectic integrators
37M15 Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
83C35 Gravitational waves
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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