On optimal canonical variables in the theory of ideal fluid with free surface

Pavel M. Lushnikov; Vladimir E. Zakharov

doi:10.1016/j.physd.2005.02.010

On optimal canonical variables in the theory of ideal fluid with free surface

Pavel M. Lushnikov, Vladimir E. Zakharov

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

12 Scopus citations

Abstract

Dynamics of ideal fluid with free surface can be effectively solved by perturbing the Hamiltonian in weak nonlinearity limit. However it is shown that perturbation theory, which includes third and fourth order terms in the Hamiltonian, results in the ill-posed equations because of short wavelength instability. To fix that problem we introduce the canonical Hamiltonian transformation from original physical variables to new variables for which instability is absent.

Original language	English (US)
Pages (from-to)	9-29
Number of pages	21
Journal	Physica D: Nonlinear Phenomena
Volume	203
Issue number	1-2
DOIs	https://doi.org/10.1016/j.physd.2005.02.010
State	Published - Apr 1 2005
Externally published	Yes

Keywords

Canonical transformation
Ill-posedness
Surface waves

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/j.physd.2005.02.010

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title = "On optimal canonical variables in the theory of ideal fluid with free surface",

abstract = "Dynamics of ideal fluid with free surface can be effectively solved by perturbing the Hamiltonian in weak nonlinearity limit. However it is shown that perturbation theory, which includes third and fourth order terms in the Hamiltonian, results in the ill-posed equations because of short wavelength instability. To fix that problem we introduce the canonical Hamiltonian transformation from original physical variables to new variables for which instability is absent.",

keywords = "Canonical transformation, Ill-posedness, Surface waves",

author = "Lushnikov, {Pavel M.} and Zakharov, {Vladimir E.}",

note = "Funding Information: Support was provided by NSF grant #DMS-0400526 (P.L.), US Army Corps of Engineers, RDT&E Programm, grant DACA #42-00-C0044 (V.Z.), and NSF grant #NDMS0072803 (V.Z.).",

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AU - Lushnikov, Pavel M.

AU - Zakharov, Vladimir E.

N1 - Funding Information: Support was provided by NSF grant #DMS-0400526 (P.L.), US Army Corps of Engineers, RDT&E Programm, grant DACA #42-00-C0044 (V.Z.), and NSF grant #NDMS0072803 (V.Z.).

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Y1 - 2005/4/1

N2 - Dynamics of ideal fluid with free surface can be effectively solved by perturbing the Hamiltonian in weak nonlinearity limit. However it is shown that perturbation theory, which includes third and fourth order terms in the Hamiltonian, results in the ill-posed equations because of short wavelength instability. To fix that problem we introduce the canonical Hamiltonian transformation from original physical variables to new variables for which instability is absent.

AB - Dynamics of ideal fluid with free surface can be effectively solved by perturbing the Hamiltonian in weak nonlinearity limit. However it is shown that perturbation theory, which includes third and fourth order terms in the Hamiltonian, results in the ill-posed equations because of short wavelength instability. To fix that problem we introduce the canonical Hamiltonian transformation from original physical variables to new variables for which instability is absent.

KW - Canonical transformation

KW - Ill-posedness

KW - Surface waves

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JF - Physica D: Nonlinear Phenomena

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ER -

On optimal canonical variables in the theory of ideal fluid with free surface

Abstract

Keywords

ASJC Scopus subject areas

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