A dynamic equation for water waves in one horizontal dimension

A. I. Dyachenko, V. E. Zakharov

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


We apply a canonical transformation to a water wave equation to remove cubic nonlinear terms and to drastically simplify fourth-order terms in the Hamiltonian. This transformation explicitly uses the vanishing exact four-wave interaction for water gravity waves for a 2D potential fluid. After transformation, the well-known but cumbersome Zakharov equation is drastically simplified and can be written in X-space in a compact form. This new equation is very suitable for analytical studies and numerical simulations.

Original languageEnglish (US)
Pages (from-to)17-21
Number of pages5
JournalEuropean Journal of Mechanics, B/Fluids
Issue number1
StatePublished - Mar 2012
Externally publishedYes


  • Free surface
  • Gravity waves
  • Zakharov equation

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)


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