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JETP Letters

, 87:667 | Cite as

Collapse of solitary waves near the transition from supercritical to subcritical bifurcations

  • D. S. Agafontsev
  • F. Dias
  • E. A. Kuznetsov
Nonlinear Dynamics

Abstract

The nonlinear stage of the instability of one-dimensional solitons within a small vicinity of the transition point from supercritical to subcritical bifurcations has been studied both analytically and numerically using the generalized nonlinear Schrödinger equation. It is shown that the pulse amplitude and its width near the collapsing time demonstrate a self-similar behavior with a small asymmetry at the pulse tails due to self-steepening. This theory is applied to solitary interfacial deep-water waves, envelope water waves with a finite depth, and short optical pulses in fibers.

PACS numbers

05.45.Yv 47.20.Ky 47.55.dr 

References

  1. 1.
    V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii, Soliton Theory (Nauka, Moscow, 1980; Plenum Press, New York, London, 1984).Google Scholar
  2. 2.
    F. Dias and G. Iooss, Eur. J. Mech. B/Fluids 15, 367 (1996).MATHMathSciNetGoogle Scholar
  3. 3.
    E. A. Kuznetsov, Zh. Éksp. Teor. Fiz. 116, 299 (1999) [JETP 89, 163 (1999)].Google Scholar
  4. 4.
    D. S. Agafontsev, F. Dias, and E. A. Kuznetsov, Pis’ma Zh. Éksp. Teor. Fiz. 83, 241 (2006) [JETP Lett. 83, 201 (2006)].Google Scholar
  5. 5.
    D. S. Agafontsev, F. Dias, and E. A. Kuznetsov, Physica D 225, 153 (2007).MATHCrossRefADSMathSciNetGoogle Scholar
  6. 6.
    G. B. Whitham, Proc. R. Soc. London, Ser. A 283, 238 (1965); J. Fluid Mech. 22, 273 (1965).MATHADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    D. S. Agafontsev, Pis’ma Zh. Éksp. Teor. Fiz. 87, 225 (2008) [JETP Lett. 87, 195 (2008)].Google Scholar
  8. 8.
    L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 4: Electrodynamics of Continuous Media (Nauka, Moscow, 1982; 2nd Eng. ed., Pergamon, London, 1984).Google Scholar
  9. 9.
    V. I. Petviashvili, Fiz. Plasmy 2, 469 (1976) [Sov. J. Plasma Phys. 2, 247 (1976)].Google Scholar
  10. 10.
    D. J. Kaup and A. C. Newell, J. Math. Phys. 19, 798 (1978).MATHCrossRefADSMathSciNetGoogle Scholar
  11. 11.
    V. E. Zakharov, Sov. Phys. JETP 35, 908 (1972).ADSGoogle Scholar
  12. 12.
    E. A. Kuznetsov, Chaos 6, 381 (1996).CrossRefADSGoogle Scholar
  13. 13.
    S. N. Vlasov, V. A. Petrishchev, and V. I. Talanov, Izv. Vyssh. Uchebn. Zaved., Radiofiz. 14, 1353 (1971) [Radiophys. Quantum Electron. 14, 1062 (1974)].Google Scholar
  14. 14.
    V. E. Zakharov, Handbook of Plasma Physics, Vol. 2: Basic Plasma Physics, Ed. by A. A. Galeev and R. N. Sudan (Elsevier, North-Holland, 1984), p. 81.Google Scholar
  15. 15.
    S. K. Turitsyn. Phys. Rev. E 47, R13 (1993).CrossRefADSMathSciNetGoogle Scholar
  16. 16.
    E. A. Kuznetsov, J. J. Rasmussen, K. Rypdal, and S. K. Turitsyn, Physica D 87, 273 (1995).CrossRefADSMathSciNetGoogle Scholar
  17. 17.
    V. E. Zakharov and V. F. Shvets, Pis’ma Zh. Éksp. Teor. Fiz. 47, 227 (1988) [JETP Lett. 47, 275 (1988)].ADSGoogle Scholar
  18. 18.
    N. A. Zharova, A. G. Litvak, and V. A. Mironov, Zh. Éksp. Teor. Fiz. 130, 21 (2006) [JETP 103, 15 (2006)].Google Scholar
  19. 19.
    A. A. Balakin, A. G. Litvak, V. A. Mironov, and S. A. Skobelev, Zh. Éksp. Teor. Fiz. 131, 408 (2007) [JETP 104, 363 (2007)].Google Scholar
  20. 20.
    G. M. Fraiman, Zh. Éksp. Teor. Fiz. 88, 390 (1985) [Sov. Phys. JETP 61, 228 (1985)].ADSMathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2008

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia
  2. 2.CMLA, ENS CachanCNRS, PRES UniverSudCachanFrance
  3. 3.Lebedev Physical InstituteMoscowRussia

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