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Solitons in Physics, Mathematics, and Nonlinear Optics

  • Conference proceedings
  • © 1990

Overview

Editors:
  1. Peter J. Olver

    1. School of Mathematics, University of Minnesota, Minneapolis, USA

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  2. David H. Sattinger

    1. School of Mathematics, University of Minnesota, Minneapolis, USA

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Part of the book series: The IMA Volumes in Mathematics and its Applications (IMA, volume 25)

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Table of contents (11 papers)

  1. Front Matter

    Pages i-xiii
    Download chapter PDF

  2. Nonlinear Evolution Equations, Inverse Scattering and Cellular Automata

    • Mark J. Ablowitz
    Pages 1-26

  3. Painlevé Equations and the Inverse Scattering and Inverse Monodromy Transforms

    • Mark J. Ablowitz
    Pages 27-43

  4. Chaotic Behavior in Nonlinear Polarization Dynamics

    • D. David, D. D. Holm, M. V. Tratnik
    Pages 45-63

  5. New Manifestations of Solitons

    • A. S. Fokas
    Pages 65-77

  6. A Unified Approach to Recursion Operators

    • A. S. Fokas, P. M. Santini
    Pages 79-96

  7. Isospectral Flows: Their Hamiltonian Structures, Miura Maps and Master Symmetries

    • Allan P. Fordy
    Pages 97-121

  8. Integrable Nonlinear Evolution Equations in the Description of Waves in the Shallow-Water Long-Wave Approximation

    • Decio Levi
    Pages 123-153

  9. Transient Solitons in Stimulated Raman Scattering

    • Curtis R. Menyuk
    Pages 155-163

  10. Monodromy Preserving Deformation of Linear Ordinary and Partial Differential Equations

    • Craig A. Tracy
    Pages 165-174

  11. Bäcklund Transformations and the Painlevé Property

    • John Weiss
    Pages 175-202

  12. Symmetry Groups of Multidimensional Integrable Nonlinear Systems

    • P. Winternitz
    Pages 203-215
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Keywords

About this book

This IMA Volume in Mathematics and its Applications SOLITONS IN PHYSICS, MATHEMATICS, AND NONLINEAR OPTICS is based on the proceedings of two workshops which were an integral part of the 1988-89 IMA program on NONLINEAR WAVES. The workshops focussed on the main parts of the theory of solitons and on the applications of solitons in physics, biology and engineering, with a special concentration on nonlinear optics. We thank the Coordinating Committee: James Glimm, Daniel Joseph, Barbara Keyfitz, An­ Majda, Alan Newell, Peter Olver, David Sattinger and David Schaeffer for drew planning and implementing the stimulating year-long program. We especially thank the Workshop Organizers for Solitons in Physics and Mathematics, Alan Newell, Peter Olver, and David Sattinger, and for Nonlinear Optics and Plasma Physics, David Kaup and Yuji Kodama for their efforts in bringing together many of the major figures in those research fields in which solitons in physics, mathematics, and nonlinear optics theories are used. A vner Friedman Willard Miller, Jr. PREFACE This volume includes some of the lectures given at two workshops, "Solitons in Physics and Mathematics" and "Solitons in Nonlinear Optics and Plasma Physics" held during the 1988-89 LM. A. year on Nonlinear Waves. Since their discovery by Kruskal and Zabusky in the early 1960's, solitons have had a profound impact on many fields, ranging from engineering and physics to algebraic geometry.

Editors and Affiliations

  • School of Mathematics, University of Minnesota, Minneapolis, USA

    Peter J. Olver, David H. Sattinger

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