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Nonlinear Equations in Physics and Mathematics

Proceedings of the NATO Advanced Study Institute held in Istanbul, Turkey, August 1–13, 1977

  • Conference proceedings
  • © 1978

Overview

Editors:
  1. A. O. Barut

    1. Department of Physics, University of Colorado, Boulder, USA

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Part of the book series: Nato Science Series C: (ASIC, volume 40)

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Table of contents (18 papers)

  1. Front Matter

    Pages i-ix
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  2. Dynamical Systems and Inverse Scattering Problems

    1. Front Matter

      Pages 1-1
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    2. Integrable Many-Body Problems

      • F. Calogero
      Pages 3-53

    3. Inverse Scattering Problems for Nonlinear Applications

      • P. C. Sabatier
      Pages 55-80

    4. Solutions of Nonlinear Equations Simulating Pair Production and Pair Annihilation

      • A. O. Barut
      Pages 81-84

    5. The Two-Time Method Applied to Slowly Evolving Oscillating Systems

      • J. Robert Buchler
      Pages 85-95

  3. Solitons

    1. Front Matter

      Pages 97-97
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    2. Solitons in Physics

      • R. K. Bullough
      Pages 99-141

    3. Solitons and Geometry

      • Fernando Lund
      Pages 143-175

    4. Hirota’s Method of Solving Soliton-Type Equations

      • P. J. Caudrey
      Pages 177-192

    5. Prolongation Structure Techniques for the New Hierarchy of Korteweg-de Vries Equations

      • R. K. Dodd
      Pages 193-204

    6. Perturbation Theory for the Double Sine-Gordon Equation

      • A. L. Mason
      Pages 205-218

  4. Discrete Systems and Continuum Mechanics

    1. Front Matter

      Pages 219-219
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    2. Painlevé Transcendents and Scaling Functions of the Two-Dimensional Ising Model

      • Craig A. Tracy
      Pages 221-237

    3. Statistical Mechanics of Nonlinear Lattice Dynamic Models Exhibiting Phase Transitions

      • T. Schneider
      Pages 239-270

    4. Nonlocal Continuum Mechanics and Some Applications

      • A. Cemal Eringen
      Pages 271-318

  5. Nonlinear Field Theories and Quantization

    1. Front Matter

      Pages 319-319
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    2. Quantization of a Nonlinear Field Equation

      • L. Castell
      Pages 321-333

    3. Characteristic “Quanta” of Nonlinear Field Equations

      • A. O. Barut
      Pages 335-345

    4. Nonlinear Schrödinger Equation with Sources: An Application of the Canonical Formalism

      • L. Girardello, R. Jengo
      Pages 347-353
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Keywords

About this book

This is the third Volume in a series of books devoted to the interdisciplinary area between mathematics and physics, all ema­ nating from the Advanced Study Institutes held in Istanbul in 1970, 1972 and 1977. We believe that physics and mathematics can develop best in harmony and in close communication and cooper­ ation with each other and are sometimes inseparable. With this goal in mind we tried to bring mathematicians and physicists together to talk and lecture to each other-this time in the area of nonlinear equations. The recent progress and surge of interest in nonlinear ordi­ nary and partial differential equations has been impressive. At the same time, novel and interesting physical applications mul­ tiply. There is a unifying element brought about by the same characteristic nonlinear behavior occurring in very widely differ­ ent physical situations, as in the case of "solitons," for exam­ ple. This Volume gives, we believe, a very good indication over all of this recent progress both in theory and applications, and over current research activity and problems. The 1977 Advanced Study Institute was sponsored by the NATO Scientific Affairs Division, The University of the Bosphorus and the Turkish Scientific and Technical Research Council. We are deeply grateful to these Institutions for their support, and to lecturers and participants for their hard work and enthusiasm which created an atmosphere of lively scientific discussions.

Editors and Affiliations

  • Department of Physics, University of Colorado, Boulder, USA

    A. O. Barut

Bibliographic Information

  • Book Title: Nonlinear Equations in Physics and Mathematics

  • Book Subtitle: Proceedings of the NATO Advanced Study Institute held in Istanbul, Turkey, August 1–13, 1977

  • Editors: A. O. Barut

  • Series Title: Nato Science Series C:

  • DOI: https://doi.org/10.1007/978-94-009-9891-9

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: D. Reidel Publishing Company, Dordrecht, Holland 1978

  • Hardcover ISBN: 978-90-277-0936-3Published: 30 November 1978

  • Softcover ISBN: 978-94-009-9893-3Published: 13 October 2011

  • eBook ISBN: 978-94-009-9891-9Published: 06 December 2012

  • Series ISSN: 1389-2185

  • Edition Number: 1

  • Number of Pages: X, 474

  • Topics: Analysis

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