Variational derivation of improved KP-type of equations

L.S.L. Lie She Liam; Embrecht W.C. van Groesen

doi:10.1016/j.physleta.2009.11.016

Variational derivation of improved KP-type of equations

L.S.L. Lie She Liam, Embrecht W.C. van Groesen

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

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Abstract

The Kadomtsev–Petviashvili equation describes nonlinear dispersive waves which travel mainly in one direction, generalizing the Korteweg–de Vries equation for purely uni-directional waves. In this Letter we derive an improved KP-equation that has exact dispersion in the main propagation direction and that is accurate in second order of the wave height. Moreover, different from the KP-equation, this new equation is also valid for waves on deep water. These properties are inherited from the AB-equation (E. van Groesen, Andonowati, 2007 [1]) which is the unidirectional improvement of the KdV equation. The derivation of the equation uses the variational formulation of surface water waves, and inherits the basic Hamiltonian structure.

Original language	Undefined
Pages (from-to)	411-415
Number of pages	5
Journal	Physics letters A
Volume	374
Issue number	3
DOIs	https://doi.org/10.1016/j.physleta.2009.11.016
Publication status	Published - 4 Jan 2010

Keywords

EWI-17265
Hamiltonian structure
KP-equation
Exact dispersion
METIS-270715
IR-69649
AB-equation
Surface water waves

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10.1016/j.physleta.2009.11.016

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Cite this

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title = "Variational derivation of improved KP-type of equations",

abstract = "The Kadomtsev–Petviashvili equation describes nonlinear dispersive waves which travel mainly in one direction, generalizing the Korteweg–de Vries equation for purely uni-directional waves. In this Letter we derive an improved KP-equation that has exact dispersion in the main propagation direction and that is accurate in second order of the wave height. Moreover, different from the KP-equation, this new equation is also valid for waves on deep water. These properties are inherited from the AB-equation (E. van Groesen, Andonowati, 2007 [1]) which is the unidirectional improvement of the KdV equation. The derivation of the equation uses the variational formulation of surface water waves, and inherits the basic Hamiltonian structure.",

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author = "{Lie She Liam}, L.S.L. and {van Groesen}, {Embrecht W.C.}",

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T1 - Variational derivation of improved KP-type of equations

AU - Lie She Liam, L.S.L.

AU - van Groesen, Embrecht W.C.

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PY - 2010/1/4

Y1 - 2010/1/4

N2 - The Kadomtsev–Petviashvili equation describes nonlinear dispersive waves which travel mainly in one direction, generalizing the Korteweg–de Vries equation for purely uni-directional waves. In this Letter we derive an improved KP-equation that has exact dispersion in the main propagation direction and that is accurate in second order of the wave height. Moreover, different from the KP-equation, this new equation is also valid for waves on deep water. These properties are inherited from the AB-equation (E. van Groesen, Andonowati, 2007 [1]) which is the unidirectional improvement of the KdV equation. The derivation of the equation uses the variational formulation of surface water waves, and inherits the basic Hamiltonian structure.

AB - The Kadomtsev–Petviashvili equation describes nonlinear dispersive waves which travel mainly in one direction, generalizing the Korteweg–de Vries equation for purely uni-directional waves. In this Letter we derive an improved KP-equation that has exact dispersion in the main propagation direction and that is accurate in second order of the wave height. Moreover, different from the KP-equation, this new equation is also valid for waves on deep water. These properties are inherited from the AB-equation (E. van Groesen, Andonowati, 2007 [1]) which is the unidirectional improvement of the KdV equation. The derivation of the equation uses the variational formulation of surface water waves, and inherits the basic Hamiltonian structure.

KW - EWI-17265

KW - Hamiltonian structure

KW - KP-equation

KW - Exact dispersion

KW - METIS-270715

KW - IR-69649

KW - AB-equation

KW - Surface water waves

U2 - 10.1016/j.physleta.2009.11.016

DO - 10.1016/j.physleta.2009.11.016

M3 - Article

SN - 0375-9601

VL - 374

SP - 411

EP - 415

JO - Physics letters A

JF - Physics letters A

IS - 3

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