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JETP Letters

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

On the nonintegrability of the free surface hydrodynamics

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

Abstract

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.

Keywords

JETP Letter Wave Interaction Envelope Soliton Nonlinear Schrodinger Equation Breather Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Supplementary material

11448_2013_280_MOESM1_ESM.pdf (92 kb)
Supplementary material, approximately 91.5 KB.

References

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    See Supplemental Material at URL to be inserted by publisher, www.jetpletters.ac.ru, v. 98,iss. 1.

Copyright information

© Pleiades Publishing, Inc. 2013

Authors and Affiliations

  • A. I. Dyachenko
    • 1
    • 2
  • 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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