Miyatake, Yuto; Yaguchi, Takaharu; Matsuo, Takayasu A multi-symplectic integration of the Ostrovsky equation. (English) Zbl 1271.65148 JSIAM Lett. 3, 41-44 (2011). 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. Cited in 1 Document 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 Keywords:Ostrovsky equation; multi-symplecticity; Preissmann box scheme; structure-preserving integration; Ostrovsky equation; gravity waves; Coriolis force; finite difference discretization; numerical example PDFBibTeX XMLCite \textit{Y. Miyatake} et al., JSIAM Lett. 3, 41--44 (2011; Zbl 1271.65148) Full Text: DOI Link