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

4 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",

note = "Funding Information: D. Dutykh would like to acknowledge the support from ERC under the research project ERC-2011-AdG 290562-MULTIWAVE and the hospitality of the Laboratory J. A. Dieudonn{\'e}, University of Nice–Sophia Antipolis during his visits. The authors acknowledge the support from CNRS under the PEPS Inphyniti 2015 project FARA. Publisher Copyright: {\textcopyright} 2015 Elsevier B.V. All rights reserved.",

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doi = "10.1016/j.physd.2015.04.001",

language = "British English",

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T1 - Numerical study of the generalised Klein-Gordon equations

AU - Dutykh, Denys

AU - Chhay, Marx

AU - Clamond, Didier

N1 - Funding Information: D. Dutykh would like to acknowledge the support from ERC under the research project ERC-2011-AdG 290562-MULTIWAVE and the hospitality of the Laboratory J. A. Dieudonné, University of Nice–Sophia Antipolis during his visits. The authors acknowledge the support from CNRS under the PEPS Inphyniti 2015 project FARA. Publisher Copyright: © 2015 Elsevier B.V. All rights reserved.

PY - 2015/5/16

Y1 - 2015/5/16

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

UR - http://www.scopus.com/inward/record.url?scp=84929378483&partnerID=8YFLogxK

U2 - 10.1016/j.physd.2015.04.001

DO - 10.1016/j.physd.2015.04.001

M3 - Article

AN - SCOPUS:84929378483

SN - 0167-2789

VL - 304-305

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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