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Partially Integrable Evolution Equations in Physics

  • Book
  • © 1990

Overview

Editors:
  1. Robert Conte

    1. Service de physique du solide et de résonance magnétique, Centre d’etudes nucléaires de Saclay, Gif-sur-Yvette, France

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  2. Nino Boccara

    1. Service de physique du solide et de résonance magnétique, Centre d’etudes nucléaires de Saclay, Gif-sur-Yvette, France

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Part of the book series: Nato Science Series C: (ASIC, volume 310)

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Table of contents (33 chapters)

  1. Front Matter

    Pages i-xvii
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  3. Instabilities and Defects

    1. Ginzburg-Landau models of non-equilibrium

      • P. Coullet, L. Gil
      Pages 261-275

    2. Nonlinear Ginzburg-Landau equation and its applications to fluid-mechanics

      • Yves Pomeau
      Pages 277-278

    3. Defects and Disorder of Non-Linear Waves in Convection

      • R. Ribotta, A. Joets
      Pages 279-296

  4. Concepts of Integrability and Singularity Analysis

    1. An Introduction to Kowalevski’s Exponents

      • D. Bessis
      Pages 299-320

    2. Singularity Analysis and its Relation to Complete, Partial and Non-Integrability

      • M. D. Kruskal, A. Ramani, B. Grammaticos
      Pages 321-372

    3. A Concept of Integrability Based on the Symmetry Approach

      • Alexandre V. Mikhailov
      Pages 373-373

    4. Bäcklund Transformations and the Painlevé property

      • John Weiss
      Pages 375-411
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Keywords

About this book

In the many physical phenomena ruled by partial differential equations, two extreme fields are currently overcrowded due to recent considerable developments: 1) the field of completely integrable equations, whose recent advances are the inverse spectral transform, the recursion operator, underlying Hamiltonian structures, Lax pairs, etc 2) the field of dynamical systems, often built as models of observed physical phenomena: turbulence, intermittency, Poincare sections, transition to chaos, etc. In between there is a very large region where systems are neither integrable nor nonintegrable, but partially integrable, and people working in the latter domain often know methods from either 1) or 2). Due to the growing interest in partially integrable systems, we decided to organize a meeting for physicists active or about to undertake research in this field, and we thought that an appropriate form would be a school. Indeed, some of the above mentioned methods are often adaptable outside their original domain and therefore worth to be taught in an interdisciplinary school. One of the main concerns was to keep a correct balance between physics and mathematics, and this is reflected in the list of courses.

Editors and Affiliations

  • Service de physique du solide et de résonance magnétique, Centre d’etudes nucléaires de Saclay, Gif-sur-Yvette, France

    Robert Conte, Nino Boccara

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