Stability of dispersion managed solitons for vanishing average dispersion
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  • 作者：Dirk Hundertmark (1)
    Peer Kunstmann (1)
    Roland Schnaubelt (1)

    1. Department of Mathematics     ; Karlsruhe Institute of Technology ; 76128 ; Karlsruhe ; Germany
  • 关键词：Primary 35Q55 ; Secondary 35B35 ; 35Q60 ; Dispersion managed nonlinear Schr枚dinger equation ; Stability ; Ground states ; Compactness
  • 刊名：Archiv der Mathematik
  • 出版年：2015
  • 出版时间：March 2015
  • 年：2015
  • 卷：104
  • 期：3
  • 页码：283-288
  • 全文大小：176 KB
  • 参考文献：1. Cazenave, T., Lions, P.L. (1982) Orbital stability of standing waves for some nonlinear Schr枚dinger equations, Comm. Math. Phys. 85: pp. 549-561 CrossRef
    2. Erdo臒an, M.B., Hundertmark, D., Lee, Y.-R. (2011) Exponential decay of dispersion management solitons, Math. Res. Lett. 18: pp. 11-24
    3. Gabitov, L., Turitsyn, S.K. (1996) Averaged pulse dynamics in a cascaded transmission system with passive dispersion compensation, Opt. Lett. 21: pp. 327-329
    4. Gabitov, L., Turitsyn, S.K. (1996) Breathing solitons in optical fiber links. JETP Lett. 63: pp. 861 CrossRef
    5. W.R. Green and D. Hundertmark, Exponential Decay for dispersion managed solitons for general dispersion profiles, Preprint, arXiv:1212.4004.
    6. Hundertmark, D., Lee, Y.-R. (2009) Decay estimates and smoothness for solutions of the dispersion managed non-linear Schr枚dinger equation, Comm. Math. Phys. 286: pp. 851-873 CrossRef
    7. Hundertmark, D., Lee, Y.-R. (2012) On non-local variational problems with lack of compactness related to non-linear optics, J. Nonlinear Sci. 22: pp. 1-38 CrossRef
    8. Kunze, M. (2004) On a variational problem with lack of compactness related to the Strichartz inequality, Calc. Var. Partial Differential Equations 19: pp. 307-336 CrossRef
    9. J. Moloney and A. Newell, Nonlinear Optics, Westview Press, Boulder (CO), 2003.
    10. Stanislalova, M. (2005) Regularity of ground state solutions of dispersion managed nonlinear Schr枚dinger equations, J. Differential Equations 210: pp. 87-105 CrossRef
    11. S.K. Turitsyn, E.G. Shapiro, S.B. Medvedev, M.P. Fedoruk, and V.K. Mezentsev, Physics and mathematics of dispersion-managed optical solitons, Comptes Rendus Physique 4 (2003), 145鈥?61.
    12. V. Zharnitsky, E. Grenier, C.K.R.T. Jones, and S.K. Turitsyn, Stabilizing effects of dispersion management, Phys. D 152鈥?53 (2001), 794鈥?17.
  • 刊物类别：Mathematics and Statistics
  • 刊物主题：Mathematics
    Mathematics
  • 出版者：Birkh盲user Basel
  • ISSN：1420-8938
文摘
We study dynamical properties of the dispersion management equation with vanishing average dispersion. Our main result establishes the stability of the set of ground states.
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