Advertisement

Solitary Waves as Fixed Points of Infinite Dimensional Maps

  • David W. McLaughlin
  • J. V. Moloney
  • A. C. Newell

Abstract

Coherent structures which are localized in space arise and play important roles in turbulent fields. Examples include tornados, large vortices in a turbulent wake, and isolated vortices in the ocean. These coherent effects are cetainly observed in nature. They can be simulated in numerical experiments and to a lesser extent in laboratory experiments. To understand such coherent phenomena analytically one must use nonlinear techniques from modern mathematics, and indeed one must extend and improve these techniques considerably.

Keywords

Solitary Wave Optical Path Length Nonlinear Medium Ring Cavity Steady State Response 
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.
    David W. McLaughlin, Solitary waves with dispersion and dissipation in: “Structure and Dynamics: Nucleic Acids and Proteins,” E. Clementi and R.H. Sarma, ed., Adenine Press, New York (1983).Google Scholar
  2. 2.
    A.S. Davydov, Energy transfer along alpha-helical proteins in: “Structure and Dynamics: Nucleic Acids and Proteins,” E. Clementi and R. H. Sarma, ed., Adenine Press, New York (1983).Google Scholar
  3. 3.
    A. C. Scott, Solitons on the alpha-helix protein in: “Structure and Dynamics: Nucleic Acids and Proteins,” E. Clementi and R. H. Sarma, ed., Adenine Press, New York (1983).Google Scholar
  4. 4.
    D.W. McLaughlin, J. V. Moloney, and A. C. Newell, Solitary waves as fixed points of infinite-dimensional maps in an optical bistable ring cavity, Phys. Rev. Lett. 51: 75 (1983).ADSCrossRefGoogle Scholar
  5. 5.
    H. Gibbs, Optical logic—what is it? where does it fit in?, Preprint, Optical Sciences Center, University of Arizona (1982).Google Scholar
  6. 6.
    M. Feigenbaumm, The transition to aperiodic behavior in turbulent systems, Comm. Math. Phys. 77: 65 (1980).MathSciNetADSCrossRefGoogle Scholar
  7. 7.
    K. Ikeda, Mutiple-valued stationary state and its instability of the transmitted light by a ring cavity system, Opt. Comm. 30: 257 (1979).ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • David W. McLaughlin
    • 1
  • J. V. Moloney
    • 1
  • A. C. Newell
    • 1
  1. 1.Department of Mathematics and Program in Applied MathematicsUniversity of ArizonaTucsonUSA

Personalised recommendations