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A Soliton as an Attractor of a Driven Damped Nonlinear Schrödinger Equation

  • N. Bekki
  • K. Nozaki
Part of the Springer Series in Synergetics book series (SSSYN, volume 30)

Abstract

Recent studies have shown that some driven damped soliton systems have a chaotic soliton exhibiting coherent spatial structure and temporal chaos [1]. These studies indicate that a low dimensional chaotic attractor corresponding to a chaotic soliton is embedded in such driven damped soliton systems. When forcing and damping effects are small enough and a forcing field consists of two oscillating components, a soliton of the nonlinear Schrödinger equation has been shown to become a chaotic attractor described by a couple of ordinary differential equations (obtained by means of the first order perturbation theory) [2].

Keywords

Chaotic Attractor Periodic Cycle Chaotic Region Point Attractor Order Perturbation Theory 
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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References

  1. 1.
    K. Nozaki and N. Bekki: Phys. Rev. Lett. 50, 1226 (1983)CrossRefGoogle Scholar
  2. A.R. Bishop, K. Fesser, P.S. Lomdahl, W.C. Kerr, M.B. Williams and S.E. Trullinger: Phys. Rev. Lett. 50, 1095 (1983)CrossRefGoogle Scholar
  3. D.W. McLaughlin, J.V. Moloney and A.C. Newell: Phys. Rev. Lett. 51, 75 (1983).CrossRefGoogle Scholar
  4. 2.
    K. Nozaki and N. Bekki: Phys. Lett. 102A, 383 (1984).CrossRefGoogle Scholar
  5. 3.
    D.J. Kaup and A.C. Newell: Phys. Rev. 818, 5162 (1978).Google Scholar
  6. 4.
    D.G. Fox and S.A. Orszag: J. Comp. Phys. 11, 612 (1973)CrossRefGoogle Scholar
  7. B. Fornberg and G.B. Whitham: Phil. Trans Roy. Soc. 289, 373 (1978).Google Scholar
  8. 5.
    For example, A.J. Lichtenberg and M.A. Lieberman: Regular and Stochastic Motion (Springer-Verlag, Berlin, 1983), P. 397.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • N. Bekki
    • 1
  • K. Nozaki
    • 1
  1. 1.Department of PhysicsNagoya UniversityNagoya 464Japan

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