Natural Hazards

, Volume 84, Supplement 2, pp 529–540 | Cite as

About compact equations for water waves

  • A. I. Dyachenko
  • D. I. Kachulin
  • V. E. Zakharov
Original Paper


A simple compact equation for gravity water waves, which includes a nonlinear wave term and advection term, is derived. Numerical simulations in the framework of this equation demonstrate an initial stage of freak wave breaking.


Nonlinear water waves Hamiltonian formalism Modulational instability Freak waves Breather 



This work was supported by Grant “Wave turbulence: theory, numerical simulation, experiment” #14-22-00174 of Russian Science Foundation.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • A. I. Dyachenko
    • 1
    • 2
  • D. I. Kachulin
    • 2
  • V. E. Zakharov
    • 1
    • 2
    • 3
    • 4
  1. 1.Landau Institute for Theoretical PhysicsChernogolovkaRussia
  2. 2.Novosibirsk State UniversityNovosibirsk-90Russia
  3. 3.Department of MathematicsUniversity of ArizonaTucsonUSA
  4. 4.Physical Institute of RASMoscowRussia

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