On galilean invariant and energy preserving bbm-type equations

Alexei Cheviakov; Denys Dutykh; Aidar Assylbekuly

doi:10.3390/sym13050878

On galilean invariant and energy preserving bbm-type equations

Alexei Cheviakov, Denys Dutykh, Aidar Assylbekuly

Mathematics

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

1 Scopus citations

Abstract

We investigate a family of higher-order BENJAMIN–BONA–MAHONY-type equations, which appeared in the course of study towards finding a GALILEI-invariant, energy-preserving long wave equation. We perform local symmetry and conservation laws classification for this family of Partial Differential Equations (PDEs). The analysis reveals that this family includes a special equation which admits additional, higher-order local symmetries and conservation laws. We compute its solitary waves and simulate their collisions. The numerical simulations show that their collision is elastic, which is an indication of its S−integrability. This particular PDE turns out to be a rescaled version of the celebrated CAMASSA–HOLM equation, which confirms its integrability.

Original language	British English
Article number	878
Journal	Symmetry
Volume	13
Issue number	5
DOIs	https://doi.org/10.3390/sym13050878
State	Published - May 2021

Keywords

BENJAMIN–BONA–MAHONY equation
Conservation laws
Nonlinear dispersive waves
Symmetries

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10.3390/sym13050878

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title = "On galilean invariant and energy preserving bbm-type equations",

abstract = "We investigate a family of higher-order BENJAMIN–BONA–MAHONY-type equations, which appeared in the course of study towards finding a GALILEI-invariant, energy-preserving long wave equation. We perform local symmetry and conservation laws classification for this family of Partial Differential Equations (PDEs). The analysis reveals that this family includes a special equation which admits additional, higher-order local symmetries and conservation laws. We compute its solitary waves and simulate their collisions. The numerical simulations show that their collision is elastic, which is an indication of its S−integrability. This particular PDE turns out to be a rescaled version of the celebrated CAMASSA–HOLM equation, which confirms its integrability.",

keywords = "BENJAMIN–BONA–MAHONY equation, Conservation laws, Nonlinear dispersive waves, Symmetries",

author = "Alexei Cheviakov and Denys Dutykh and Aidar Assylbekuly",

note = "Funding Information: Funding: A.C. is grateful to NSERC of CANADA for research support through the Discovery grant program. D.D. acknowledges support from the F{\'e}d{\'e}ration de Recherche en Math{\'e}matiques AUVERGNE– RH{\^O}NE–ALPES (FR 3490). The work of D.D. has also been supported by the French National Research Agency, through Investments for Future Program (ref. ANR−18−EURE−0016—Solar Academy). The research of A.A. was supported by KAZAKHSTAN Ministry of Education and Science (AP08053154). Publisher Copyright: {\textcopyright} 2021 by the authors. Licensee MDPI, Basel, Switzerland.",

year = "2021",

month = may,

doi = "10.3390/sym13050878",

language = "British English",

volume = "13",

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AU - Cheviakov, Alexei

AU - Dutykh, Denys

AU - Assylbekuly, Aidar

N1 - Funding Information: Funding: A.C. is grateful to NSERC of CANADA for research support through the Discovery grant program. D.D. acknowledges support from the Fédération de Recherche en Mathématiques AUVERGNE– RHÔNE–ALPES (FR 3490). The work of D.D. has also been supported by the French National Research Agency, through Investments for Future Program (ref. ANR−18−EURE−0016—Solar Academy). The research of A.A. was supported by KAZAKHSTAN Ministry of Education and Science (AP08053154). Publisher Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2021/5

Y1 - 2021/5

N2 - We investigate a family of higher-order BENJAMIN–BONA–MAHONY-type equations, which appeared in the course of study towards finding a GALILEI-invariant, energy-preserving long wave equation. We perform local symmetry and conservation laws classification for this family of Partial Differential Equations (PDEs). The analysis reveals that this family includes a special equation which admits additional, higher-order local symmetries and conservation laws. We compute its solitary waves and simulate their collisions. The numerical simulations show that their collision is elastic, which is an indication of its S−integrability. This particular PDE turns out to be a rescaled version of the celebrated CAMASSA–HOLM equation, which confirms its integrability.

AB - We investigate a family of higher-order BENJAMIN–BONA–MAHONY-type equations, which appeared in the course of study towards finding a GALILEI-invariant, energy-preserving long wave equation. We perform local symmetry and conservation laws classification for this family of Partial Differential Equations (PDEs). The analysis reveals that this family includes a special equation which admits additional, higher-order local symmetries and conservation laws. We compute its solitary waves and simulate their collisions. The numerical simulations show that their collision is elastic, which is an indication of its S−integrability. This particular PDE turns out to be a rescaled version of the celebrated CAMASSA–HOLM equation, which confirms its integrability.

KW - BENJAMIN–BONA–MAHONY equation

KW - Conservation laws

KW - Nonlinear dispersive waves

KW - Symmetries

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JO - Symmetry

JF - Symmetry

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ER -

On galilean invariant and energy preserving bbm-type equations

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Keywords

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