JETP Letters

, Volume 98, Issue 1, pp 43–47 | Cite as

On the nonintegrability of the free surface hydrodynamics

  • A. I. DyachenkoEmail author
  • D. I. Kachulin
  • V. E. Zakharov
Nonlinear Dynamics


The integrability of the compact 1D Zakharov equation has been analyzed. The numerical experiments show that the multiple collisions of breathers (which correspond to envelope solitons in the NLSE approximation) are not pure elastic. The amplitude of six-wave interactions for the compact 1D Zakharov equation has also been analyzed. It has been found that the six-wave amplitude is not canceled for this equation. Thus, the 1D Zakharov equation is not integrable.


JETP Letter Wave Interaction Envelope Soliton Nonlinear Schrodinger Equation Breather Solution 
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Supplementary material

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Copyright information

© Pleiades Publishing, Inc. 2013

Authors and Affiliations

  • A. I. Dyachenko
    • 1
    • 2
    Email author
  • D. I. Kachulin
    • 2
  • V. E. Zakharov
    • 1
    • 2
    • 3
    • 4
  1. 1.Novosibirsk State UniversityNovosibirskRussia
  2. 2.Landau Institute for Theoretical PhysicsRussian Academy of SciencesChernogolovka, Moscow regionRussia
  3. 3.Department of MathematicsUniversity of ArizonaTucsonUSA
  4. 4.Lebedev Physical InstituteRussian Academy of SciencesMoscowRussia

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