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

Angel Durán; Denys Dutykh; Dimitrios Mitsotakis

doi:10.1016/j.physd.2019.05.002

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

Angel Durán
, Denys Dutykh
, Dimitrios Mitsotakis

Mathematics

Universidad de Valladolid
Victoria University of Wellington

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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 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 language	British English
Pages (from-to)	1-16
Number of pages	16
Journal	Physica D: Nonlinear Phenomena
Volume	397
DOIs	https://doi.org/10.1016/j.physd.2019.05.002
State	Published - Oct 2019

Keywords

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

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10.1016/j.physd.2019.05.002

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title = "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 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.",

keywords = "Boussinesq equations, Geometric numerical integration, Multi-symplectic schemes, Surface waves, Symplectic methods",

author = "Angel Dur{\'a}n and Denys Dutykh and Dimitrios Mitsotakis",

note = "Funding Information: AD was supported by Junta de Castilla y Leon and Fondos FEDER under the Grant VA041P17 . DM{\textquoteright}s work was supported by the Marsden Fund administered by the Royal Society of New Zealand with contract number VUW1418 . AD and DM would like to acknowledge the support from the University Savoie Mont Blanc and the hospitality of LAMA UMR \#5127 during their respective visits in 2019. Publisher Copyright: {\textcopyright} 2019 Elsevier B.V.",

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doi = "10.1016/j.physd.2019.05.002",

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AU - Dutykh, Denys

AU - Mitsotakis, Dimitrios

N1 - Funding Information: AD was supported by Junta de Castilla y Leon and Fondos FEDER under the Grant VA041P17 . DM’s work was supported by the Marsden Fund administered by the Royal Society of New Zealand with contract number VUW1418 . AD and DM would like to acknowledge the support from the University Savoie Mont Blanc and the hospitality of LAMA UMR #5127 during their respective visits in 2019. Publisher Copyright: © 2019 Elsevier B.V.

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N2 - 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.

AB - 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.

KW - Boussinesq equations

KW - Geometric numerical integration

KW - Multi-symplectic schemes

KW - Surface waves

KW - Symplectic methods

UR - https://www.scopus.com/pages/publications/85066263903

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DO - 10.1016/j.physd.2019.05.002

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JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

ER -

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

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Keywords

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