Partially Integrable Evolution Equations in Physics

1. Front Matter

   Pages i-xvii

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2. Waves in Physical Systems

   1. Competing Interactions and Complexity in Condensed Matter

      • A. R. Bishop

      Pages 1-38

   2. Exact Solutions of the Boltzmann Equation

      • H. Cornille

      Pages 39-82

   3. Nonlinear Interaction Between Short and Long Waves

      • V. I. Karpman

      Pages 83-159

   4. Nonlinear Optics

      • Alan C. Newell, J. V. Moloney

      Pages 161-161

   5. The Phase Diffusion and Mean Drift Equations for Convection at Finite Rayleigh Numbers in Large Containers I

      • Alan C. Newell, Thierry Passot, Mohammad Souli

      Pages 163-163

   6. Nonlinear Evolution Equations, Quasi-Solitons and their Experimental Manifestation

      • M. Remoissenet

      Pages 165-221

   7. The Initial-Boundary Value Problem for the Davey-Stewartson 1 Equation; How to Generate and Drive Localized Coherent Structures in Multidimensions

      • P. M. Santini, A. S. Fokas

      Pages 223-259

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

5. Mathematical Methods

   1. Differential Geometry Techniques for Sets of Nonlinear Partial Differential Equations

      • Frank B. Estabrook

      Pages 413-434

   2. Inertial Manifolds and Attractors of Partial Differential Equations

      • J. M. Ghidaglia

      Pages 435-458

   3. Hirota’s Bilinear Method and Partial Integrability

      • J. Hietarinta

      Pages 459-478

   4. Generalized Symmetries, Recursion Operators and Bihamiltonian Systems

      • Y. Kosmann-Schwarzbach

      Pages 479-489

   5. Nonlinear Dispersive Equations without Inverse Scattering

      • Jean-Claude Saut

      Pages 491-513

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.

• Boundary value problem
• Operator
• Potential
• Soliton
• Transformation
• calculus
• geometry
• mechanics
• modeling
• partial differential equation
• partial differential equations

• 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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