Numerical study of the generalised Klein-Gordon equations

Denys Dutykh; Marx Chhay; Didier Clamond

doi:10.1016/j.physd.2015.04.001

Numerical study of the generalised Klein-Gordon equations

Denys Dutykh
, Marx Chhay
, Didier Clamond

Mathematics

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

5 Scopus citations

Abstract

In this study, we discuss an approximate set of equations describing water wave propagating in deep water. These generalised Klein-Gordon (gKG) equations possess a variational formulation, as well as a canonical Hamiltonian and multi-symplectic structures. Periodic travelling wave solutions are constructed numerically to high accuracy and compared to a seventh-order Stokes expansion of the full Euler equations. Then, we propose an efficient pseudo-spectral discretisation, which allows to assess the stability of travelling waves and localised wave packets.

Original language	British English
Pages (from-to)	23-33
Number of pages	11
Journal	Physica D: Nonlinear Phenomena
Volume	304-305
DOIs	https://doi.org/10.1016/j.physd.2015.04.001
State	Published - 16 May 2015

Keywords

Deep water approximation
Periodic waves
Spectral methods
Stability
Travelling waves

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10.1016/j.physd.2015.04.001

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title = "Numerical study of the generalised Klein-Gordon equations",

abstract = "In this study, we discuss an approximate set of equations describing water wave propagating in deep water. These generalised Klein-Gordon (gKG) equations possess a variational formulation, as well as a canonical Hamiltonian and multi-symplectic structures. Periodic travelling wave solutions are constructed numerically to high accuracy and compared to a seventh-order Stokes expansion of the full Euler equations. Then, we propose an efficient pseudo-spectral discretisation, which allows to assess the stability of travelling waves and localised wave packets.",

keywords = "Deep water approximation, Periodic waves, Spectral methods, Stability, Travelling waves",

author = "Denys Dutykh and Marx Chhay and Didier Clamond",

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AU - Chhay, Marx

AU - Clamond, Didier

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PY - 2015/5/16

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N2 - In this study, we discuss an approximate set of equations describing water wave propagating in deep water. These generalised Klein-Gordon (gKG) equations possess a variational formulation, as well as a canonical Hamiltonian and multi-symplectic structures. Periodic travelling wave solutions are constructed numerically to high accuracy and compared to a seventh-order Stokes expansion of the full Euler equations. Then, we propose an efficient pseudo-spectral discretisation, which allows to assess the stability of travelling waves and localised wave packets.

AB - In this study, we discuss an approximate set of equations describing water wave propagating in deep water. These generalised Klein-Gordon (gKG) equations possess a variational formulation, as well as a canonical Hamiltonian and multi-symplectic structures. Periodic travelling wave solutions are constructed numerically to high accuracy and compared to a seventh-order Stokes expansion of the full Euler equations. Then, we propose an efficient pseudo-spectral discretisation, which allows to assess the stability of travelling waves and localised wave packets.

KW - Deep water approximation

KW - Periodic waves

KW - Spectral methods

KW - Stability

KW - Travelling waves

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DO - 10.1016/j.physd.2015.04.001

M3 - Article

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SP - 23

EP - 33

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

ER -

Numerical study of the generalised Klein-Gordon equations

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Keywords

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