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 Scopus citations


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
Issue number1-2
StatePublished - Apr 1 2005



  • 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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