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Solitons, Nonlinear Evolution Equations and Inverse Scattering

Solitons, Nonlinear Evolution Equations and Inverse Scattering

$160.00 (P)

Part of London Mathematical Society Lecture Note Series

  • Date Published: January 1992
  • availability: Available
  • format: Paperback
  • isbn: 9780521387309

$ 160.00 (P)
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About the Authors
  • This book brings together several aspects of soliton theory currently available only in research papers. Emphasis is given to the multi-dimensional problems which arise and includes inverse scattering in multi-dimensions, integrable nonlinear evolution equations in multi-dimensions and the dbar method.

    • Ablowitz is one of the founders of soliton theory
    • Soliton theory is one of the new growth areas in mathematics, one of the most important ways of solving partial differential equations
    • Soliton books sell
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    Reviews & endorsements

    "...well-written and presented." R. Grimshaw, Journal of Fluid Mechanics

    "For researchers working in this [field] this book is a valuable source of information which provides an excellent overview of the established results and the present developments. The presentation is clear and well structured, so that novices wishing to move into inverse scattering and solitons will find this book to be a useful introduction to these modern techniques." Walter Oevel, Mathematical Reviews

    "...reflects the changing emphasis of current research into solitons and integrable systems by concentrating on systems with more than one space dimension....valuable in bridging the diverse approaches to the subject by analysts and algebraic geometers. It records the relationships between results of gauge theory, Lie algebras and functional analysis and those of classical and numerical analysis....a well-ordered treasure house of ancient and modern work on integrable systems, fascinating and useful to browse in...essential for all specialists on integrable systems and for all major mathematical libraries." P.G. Drazin, Bulletin of the London Mathematical Society

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    Product details

    • Date Published: January 1992
    • format: Paperback
    • isbn: 9780521387309
    • length: 532 pages
    • dimensions: 229 x 152 x 34 mm
    • weight: 0.784kg
    • contains: 58 b/w illus. 1 table
    • availability: Available
  • Table of Contents

    1. Introduction
    2. Inverse scattering for the Korteweg-de Vries equation
    3. General inverse scattering in one dimension
    4. Inverse scattering for integro-differential equations
    5. Inverse scattering in two dimensions
    6. Inverse scattering in multidimensions
    7. The Painleve equations
    8. Discussion and open problems
    Appendix A: Remarks on Riemann-Hilbert problems
    Appendix B: Remarks on problems
    References
    Subject index
    Author index.

  • Authors

    M. A. Ablowitz, University of Colorado, Boulder

    P. A. Clarkson, University of Exeter

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