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

Pavel M. Lushnikov, Vladimir E Zakharov

Research output: Contribution to journalArticle

12 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)9-29
Number of pages21
JournalPhysica D: Nonlinear Phenomena
Volume203
Issue number1-2
DOIs
StatePublished - Apr 1 2005

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ideal fluids
Hamiltonians
Ideal Fluid
Free Surface
Fluids
fixing
perturbation theory
nonlinearity
Perturbation Theory
Fourth Order
wavelengths
Nonlinearity
Wavelength
Term

Keywords

  • Canonical transformation
  • Ill-posedness
  • Surface waves

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

On optimal canonical variables in the theory of ideal fluid with free surface. / Lushnikov, Pavel M.; Zakharov, Vladimir E.

In: Physica D: Nonlinear Phenomena, Vol. 203, No. 1-2, 01.04.2005, p. 9-29.

Research output: Contribution to journalArticle

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