About shape of giant breather

V. E. Zakharov, A. I. Dyachenko

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)


The pulse of freak waves on the surface of deep water can be a breather-type solution of the Euler equation. The shape of surface is periodic function of time in a moving frame. Only in the limit of very small steepness its shape is described by the Nonlinear Shredinger Equation (NLSE). For moderately small steepness we derived more exact envelope nonlocal equation similar to well-known Dysthe equation (DE), which is more convenient for analytical and numerical study. We have found approximate solution of this equation by the use of the variational approach.

Original languageEnglish
Pages (from-to)127-131
Number of pages5
JournalEuropean Journal of Mechanics, B/Fluids
Issue number2
Publication statusPublished - Mar 2010
Externally publishedYes


  • Dysthe equation
  • freak wave
  • free surface


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