Advertisement

Radiophysics and Quantum Electronics

, Volume 58, Issue 3, pp 209–215 | Cite as

Solitons in an Extended Nonlinear Schrödinger Equation with Pseudo Stimulated Scattering and Inhomogeneous Cubic Nonlinearity

  • N. V. AseevaEmail author
  • E. M. Gromov
  • V. V. Tyutin
Article
  • 30 Downloads

We consider the soliton dynamics within the framework of an extended nonlinear Schrödinger equation with pseudo stimulated scattering, which occurs from the damped low-frequency waves, and the spatially inhomogeneous cubic nonlinearity. It is shown that the pseudo stimulated scattering, which leads to a shift of the spectrum of the soliton wave numbers to the long-wavelength region, and the nonlinearity, which increases with the coordinate and shifts the soliton spectrum to the short-wavelength region, can be in balance. The soliton solution, which results from this balance, is explicitly obtained.

Keywords

Soliton Wave Packet Soliton Solution Raman Stimulate Scattering Envelope Function 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E. Infeld and G.Rowlands, Nonlinear Waves, Solitons, and Chaos, Cambridge Univ. Press, Cambridge (2000).Google Scholar
  2. 2.
    G.P. Agrawal, Nonlinear Fiber Optics, Academic Press, San Diego (2001).Google Scholar
  3. 3.
    Y.Yang, Solitons in Field Theory and Nonlinear Analysis, Springer, New York (2001).Google Scholar
  4. 4.
    Y. S. Kivshar and G.P.Agrawal, Optical Solitons: From Fibers to Photonic Crystals, Academic Press, San Diego (2003).Google Scholar
  5. 5.
    L. A. Dickey, Soliton Equation and Hamiltonian Systems, World Scientific, New York (2005).Google Scholar
  6. 6.
    B. A. Malomed, Soliton Management in Periodic Systems, Springer, New York (2006).zbMATHGoogle Scholar
  7. 7.
    T. Dauxois and M.Peyrard, Physics of Solitons, Cambridge Univ. Press, Cambridge (2006).Google Scholar
  8. 8.
    J.P. Gordon, Opt. Lett., 11, 662 (1986).CrossRefADSGoogle Scholar
  9. 9.
    F. M. Mitschke and L. F.Mollenauer, Opt. Lett., 11, 659 (1986).Google Scholar
  10. 10.
    Y. J. Kodama, Stat. Phys., 39, 597 (1985).MathSciNetCrossRefADSGoogle Scholar
  11. 11.
    B. A. Malomed and R. S.Tasgal, J. Opt. Soc. Am. B, 15, 162 (1998).Google Scholar
  12. 12.
    F. Biancalama, D.V. Skrybin, and A. V.Yulin, Phys. Rev. E, 70, 011615 (2004).Google Scholar
  13. 13.
    R.-J. Essiambre and G. P. Agrawal, J. Opt. Soc. Am. B, 14, 314 (1997).CrossRefADSGoogle Scholar
  14. 14.
    R.-J. Essiambre and G. P. Agrawal, J. Opt. Soc. Am. B, 14, 323 (1997).CrossRefADSGoogle Scholar
  15. 15.
    A.Andrianov, S.Muraviev, A.Kim, and A. Sysoliatin, Laser Phys., 17, 1296 (2007).Google Scholar
  16. 16.
    S. Chernikov, E.Dianov, D.Richardson, and D. Payne, Opt. Lett., 18, 476 (1993).Google Scholar
  17. 17.
    E. M. Gromov and B.A.Malomed, J. Plasma Phys., 79, 1057 (2013).Google Scholar
  18. 18.
    E. M. Gromov and B.A.Malomed, Opt. Commun., 320, 88 (2014).Google Scholar
  19. 19.
    N. V. Aseeva, E. M. Gromov, and V. V.Tyutin, Radiophys. Quantum Electron., 56, No. 3, 157 (2013).Google Scholar
  20. 20.
    V.E. Zakharov and V. E.Kuznetsov, Physics—Uspekhi, 40, No. 11, 1087 (1997).Google Scholar
  21. 21.
    V.E. Zakharov, Radiophys. Quantum Electron., 17, No. 4, 326 (1974).CrossRefADSGoogle Scholar
  22. 22.
    V. A. Bogatyrev, M.M.Bubnov, et al., J. Lightwave Technol., 9, 561 (1991).Google Scholar
  23. 23.
    R. Blit and B.A.Malomed, Phys. Rev. A, 86, 043841 (2012).Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.National Research University “Higher School of Economics,”Nizhny NovgorodRussia

Personalised recommendations