Freak-Waves: Compact Equation Versus Fully Nonlinear One

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


We compare applicability of the recently derived compact equation for surface wave with the fully nonlinear equations. Strongly nonlinear phenomena, namely modulational instability and breathers with the steepness \(\mu \sim 0.4\) are compared in numerical simulations using both models.



Main part of this work, regarding numerical simulation of modulational instability and narrow breather in the framework of compact equation and derivation of canonical transformation, was supported by Grant “Wave turbulence: theory, numerical simulation, experiment” #14-22-00174 of Russian Science Foundation.

Rest part of the work was supported by the Program “Fundamental Problems of Nonlinear Dynamics in Mathematics and Physics” from the RAS Presidium, and Grant 6170.2012.2 “Leading Scientific Schools of Russia”.

Numerical simulation was performed on the Informational Computational Center of the Novosibirsk State University.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • A. I. Dyachenko
    • 1
    • 2
  • D. I. Kachulin
    • 2
  • V. E. Zakharov
    • 2
    • 3
    • 4
    • 5
  1. 1.Landau Institute for Theoretical Physics RASChernogolovkaRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia
  3. 3.Department of MathematicsUniversity of ArizonaTucsonUSA
  4. 4.Physical Institute of RASMoscowRussia
  5. 5.Landau Institute for Theoretical PhysicsMoscowRussia

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