Water waves and integrability

Rossen I. Ivanov

doi:10.1098/rsta.2007.2007

Water waves and integrability

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

Abstract

Euler's equations describe the motion of inviscid fluid. In the case of shallow water, when a perturbative asymptotic expansion of Euler's equations is considered (to a certain order of smallness of the scale parameters), relations to certain integrable equations emerge. Some recent results concerning the use of integrable equation in modelling the motion of shallow water waves are reviewed in this contribution.

Original language	English
Pages (from-to)	2267-2280
Number of pages	14
Journal	Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	365
Issue number	1858
DOIs	https://doi.org/10.1098/rsta.2007.2007
Publication status	Published - 13 Mar 2007
Externally published	Yes

Keywords

Camassa-Holm equation
Degasperis-Procesi equation
Euler's equations
Integrability
Korteweg-de Vries equation

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10.1098/rsta.2007.2007

https://arrow.tudublin.ie/scschmatart/96Licence: CC BY-NC-SA

Cite this

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title = "Water waves and integrability",

abstract = "Euler's equations describe the motion of inviscid fluid. In the case of shallow water, when a perturbative asymptotic expansion of Euler's equations is considered (to a certain order of smallness of the scale parameters), relations to certain integrable equations emerge. Some recent results concerning the use of integrable equation in modelling the motion of shallow water waves are reviewed in this contribution.",

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AB - Euler's equations describe the motion of inviscid fluid. In the case of shallow water, when a perturbative asymptotic expansion of Euler's equations is considered (to a certain order of smallness of the scale parameters), relations to certain integrable equations emerge. Some recent results concerning the use of integrable equation in modelling the motion of shallow water waves are reviewed in this contribution.

KW - Camassa-Holm equation

KW - Degasperis-Procesi equation

KW - Euler's equations

KW - Integrability

KW - Korteweg-de Vries equation

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U2 - 10.1098/rsta.2007.2007

DO - 10.1098/rsta.2007.2007

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JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

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ER -

Water waves and integrability

Abstract

Keywords

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