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On the multi-symplectic structure of Boussinesq-type systems. II: Geometric discretization

Abstract : In this paper we consider the numerical approximation of systems of Boussinesq-type to model surface wave propagation. Some theoretical properties of these systems (multi-symplectic and Hamiltonian formulations, well-posedness and existence of solitary-wave solutions) were previously analyzed by the authors in Part I. As a second part of the study, considered here is the construction of geometric schemes for the numerical integration. By using the method of lines, the geometric properties, based on the multi-symplectic and Hamiltonian structures, of different strategies for the spatial and time discretizations are discussed and illustrated.
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Angel Durán, Denys Dutykh, Dimitrios Mitsotakis. On the multi-symplectic structure of Boussinesq-type systems. II: Geometric discretization. Physica D: Nonlinear Phenomena, Elsevier, 2019, 397, pp.1-16. ⟨10.1016/j.physd.2019.05.002⟩. ⟨hal-02123559⟩

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