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

Angel Durán, Denys Dutykh, Dimitrios Mitsotakis

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2 Scopus citations


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 analysed 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.

Original languageBritish English
Pages (from-to)1-16
Number of pages16
JournalPhysica D: Nonlinear Phenomena
StatePublished - Oct 2019


  • Boussinesq equations
  • Geometric numerical integration
  • Multi-symplectic schemes
  • Surface waves
  • Symplectic methods


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