Solitons in physics, mathematics, and nonlinear optics

Author(s)

• Olver, Peter J.
• Sattinger, David H.
• IMA Program on Nonlinear Waves
• Workshop, "Solitons in Physics and Mathematics"
• Workshop, "Solitons in Nonlinear Optics and Plasma Physics"

Bibliographic Information

Solitons in physics, mathematics, and nonlinear optics

Peter J. Olver, David H. Sattinger, editors

（The IMA volumes in mathematics and its applications, v. 25）

Springer-Verlag, c1990

• : us
• : gw

Note

"Proceedings of two workshops which were an integral part of the 1988-89 IMA program on NONLINEAR WAVES" -- Foreword

"Two workshops, "Solitons in Physics and Mathematics" and "Solitons in Nonlinear Optics and Plasma Physics" held during the 1988-89 I.M.A. year on Nonlinear Waves" -- Pref

Includes bibliographical references

Contents of Works

• Nonlinear evolution equations, inverse scattering, and cellular automata / Mark J. Ablowitz
• Painlevé equations and the inverse scattering and inverse monodromy transforms / Mark J. Ablowitz
• Chaotic behavior in nonlinear polarization dynamics / D. David, D.D. Holm, and M.V. Tratnik
• New manifestations of solitons / A.S. Fokas
• A unified approach to recursion operators / A.S. Fokas and P.M. Santini
• Isospectral flows / Allan P. Fordy
• Integrable nonlinear evolution equations in the description of waves in the shallow-water long-wave approximation / Decio Levi
• Transient solitons in stimulated Raman scattering / Curtis R. Menyuk
• Monodromy preserving deformation of linear ordinary and partial differential equations / Craig A. Tracy
• Bäcklund transformations and the Painlevé property / John Weiss
• Symmetry groups of multidimensional integrable nonlinear systems / P. Winternitz

Description and Table of Contents

Volume

: us ISBN 9780387973098

Description

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."

Volume

: gw ISBN 9783540973096

Description

This volume includes some of the letters given at two workshops, "Solitons in Physics and Mathematics" and "Solitons in Nonlinear Optics and Plasma Physics", held during 1988 and 1989. Since their discovery by Kruskal and Zabusky in the early 1960s, solitons have had a profound impact on many fields, ranging from engineering and physics to algebraic geometry. The present contributions represent only a fraction of these areas, but give the reader a good overview of several research directions, including optics, fluid dynamics, inverse scattering, cellular automata, Backlund equations, symmetries and Hamiltonian systems.

Table of Contents

• Nonlinear evolution equations, inverse scattering and cellular automata
• equations and the inverse scattering and inverse monodromy transforms
• chaotic behaviour in nonlinear polarization dynamics
• new manifestations of solitons
• a unified approach to recursion operators
• isospectral flows - their Hamiltonian structures, Miura maps and master symmetries
• integrable nonlinear evolution equation in the description of waves in the shallow-water long-wave approximation
• transient solitons in stimulated Raman scattering
• monodromy preserving deformation on linear ordinary and partial differential equations
• Backlund property
• symmetry groups of multidimensional integrable nonlinear systems.

by "Nielsen BookData"

Details

• NCID: BA10727086
• ISBN:
  • 0387973095
  • 3540973095
• LCCN: 90009741
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: New York ; Berlin
• Pages/Volumes: vii, 215 p.
• Size: 25 cm
• Classification:
  • LCC : QC174.26.W28
  • DC20 : 530.1/4
  • NDC8 : 421.5
  • NDLC : MC43
• Subject Headings:
  • LCSH : Solitons -- Congresses
  • LCSH : Nonlinear optics -- Congresses
  • LCSH : Evolution equations, Nonlinear -- Congresses
• Parent Bibliography ID:
  • BA00327784