Hard soliton excitation regime: Stability investigation

  • E. A. Kuznetsov
Nonlinear Physics

Abstract

The problem of the stability of one-dimensional solitons in the hard regime of soliton excitation, where the matrix element of the four-wave interaction has an additional smallness, is studied. It is that shown for optical solitons striction can weaken the Kerr nonlinearity. It is shown that solitons with a finite amplitude discontinuity at the critical soliton velocity, equal to the minimum phase velocity of linear waves, are unstable while solitons with a soft transition remain stable with respect to one-dimensional perurbations. Two-and three-dimensional solitons near threshold are unstable with respect to modulation perturbations.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. S. Loguet-Higgins, J. Fluid Mech. 200, 951 (1989).Google Scholar
  2. 2.
    G. Iooss and K. Kirchgassner, C. R. Acad. Sci. Paris 311, I, 265 (1991).MathSciNetGoogle Scholar
  3. 3.
    J.-M. Vanden-Broeck and F. Dias, J. Fluid Mech. 240, 549 (1992); F. Dias and G. Iooss, Physica D 65, 399 (1993).ADSMathSciNetGoogle Scholar
  4. 4.
    M. S. Loguet-Higgins, J. Fluid Mech. 252, 703 (1993).ADSMathSciNetGoogle Scholar
  5. 5.
    V. E. Zakharov and E. A. Kuznetsov, Zh. Éksp. Teor. Fiz. 113, 1892 (1998) [JETP 86, 1035 (1998)].Google Scholar
  6. 6.
    L. D. Landau, Dokl. Akad. Nauk 44, 339 (1944); L. D. Landau and E. M. Lifshitz, The Theory of Elasticity, 3rd English edition (Pergamon Press, New York, 1986) [Russian original, Nauka, Moscow, 1953].Google Scholar
  7. 7.
    F. Dias and G. Iooss, Eur. J. Mech. B/Fluids 15, 367 (1996).MathSciNetGoogle Scholar
  8. 8.
    V. E. Zakharov and E. A. Kuznetsov, Usp. Fiz. Nauk 167, 1 (1997).Google Scholar
  9. 9.
    G. Iooss, C. R. Acad. Sci. Paris 324, 993 (1997).MATHMathSciNetGoogle Scholar
  10. 10.
    L. D. Landau and E. M. Lifshitz, Statistical Physis, Part 1 (Pergamon Press, New York) [Russian original, Nauka, Moscow, 1995, p. 521).Google Scholar
  11. 11.
    E. A. Kuznetsov and S. K. Turitsyn, Phys. Lett. A 112, 273 (1985).CrossRefADSGoogle Scholar
  12. 12.
    E. I. Kats, V. V. Lebedev, and A. R. Muratov, Phys. Rep. 228, 1 (1993).CrossRefADSGoogle Scholar
  13. 13.
    N. G. Vakhitov and A. A. Kolokolov, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 16, 1020 (1973).Google Scholar
  14. 14.
    E. A. Kuznetsov, Phys. Lett. A 101, 314 (1983).ADSGoogle Scholar
  15. 15.
    J. Nycander, Chaos 4, 253 (1994).CrossRefADSGoogle Scholar
  16. 16.
    E. M. Gromov and V. I. Talanov, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 39, 735 (1996); Zh. Éksp. Teor. Fiz. 110, 137 (1996) [JETP 83, 73 (1996)].MathSciNetGoogle Scholar
  17. 17.
    V. E. Zakharov and A. B. Shabat, Zh. Éksp. Teor. Fiz. 61, 118 (1971) [Sov. Phys. JETP 34, 62 (1972)].Google Scholar
  18. 18.
    V. E. Zakharov, in Handbook of Plasma Physics, Vol. 2, Basic Plasma Physics II, edited by A. Galeev and R. Sudan (North-Holland, Amsterdam, 1984), p. 81.Google Scholar
  19. 19.
    A. C. Newell, Solitons in Mathematics and Physics (SIAM, Philadelphia, 1985).Google Scholar
  20. 20.
    E. A. Kuznetsov, A. M. Rubenchik, and V. E. Zakharov, Phys. Rep. 142, 103 (1986).CrossRefADSMathSciNetGoogle Scholar
  21. 21.
    E. A. Kuznetsov, J. J. Rasmussen, K. Rypdal, and S. K. Turitsyn, Physica D 87, 273 (1995).MathSciNetGoogle Scholar
  22. 22.
    E. A. Kuznetsov, Chaos 6, 381 (1996).CrossRefADSGoogle Scholar
  23. 23.
    N. Bloembergen, Nonlinear Optics, (Benjamin, Reading, MA 1977).Google Scholar
  24. 24.
    G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, Boston, 1989) [Russian translation, Mir, Moscow, 1996).Google Scholar
  25. 25.
    L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon Press, New York) [Russian original, Nauka, Moscow, 1982].Google Scholar
  26. 26.
    V. E. Zakharov and A. M. Rubenchik, Prikl. Mekh. Tekh. Fiz. 13, 669 (1974).Google Scholar

Copyright information

© American Institute of Physics 1999

Authors and Affiliations

  • E. A. Kuznetsov
    • 1
  1. 1.L. D. Landau Institute of Theoretical PhysicsRussian Academy of SciencesMoscowRussia

Personalised recommendations