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Direct and Inverse Methods in Nonlinear Evolution Equations

Lectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, September 5–12, 1999

  • Book
  • © 2003

Overview

Authors:
  1. Robert M. Conte

    1. l'Etat Condensé (SPEC), CEA Saclay Service de Physique de, Gif-sur-Yvette CX, France

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  2. Franco Magri

    1. Università Milano-Bicocca Dipto. Matematica e Applicazioni, Milano, Italy

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  3. Micheline Musette

    1. Dept. Natuurkunde (DNTK), Vrije Universiteit Brussel Fak. Wetenschappen, Bruxelles, Belgium

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  4. Junkichi Satsuma

    1. Mathematical Sciences, University of Tokyo Graduate School of, Tokyo, Japan

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  5. Pavel Winternitz

    1. Université de Montréal Centre de Recherches Mathématiques, Montreal, Canada

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Editors:
  1. Antonio Maria Greco

    1. Università di Palermo Dipto. Matematica ed Applicazioni, Palermo, Italy

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Part of the book series: Lecture Notes in Physics (LNP, volume 632)

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Table of contents (5 chapters)

  1. Front Matter

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  2. Exact solutions of nonlinear partial differential equations by singularity analysis

    • Robert Conte
    Pages 1-83

  3. The method of Poisson pairs in the theory of nonlinear PDEs

    • Franco Magri, Gregorio Falqui, Marco Pedroni
    Pages 85-136

  4. Nonlinear superposition formulae of integrable partial differential equations by the singular manifold method

    • Micheline Musette
    Pages 137-170

  5. Hirota bilinear method for nonlinear evolution equations

    • Junkichi Satsuma
    Pages 171-222

  6. Lie groups, singularities and solutions of nonlinear partial differential equations

    • Pavel Winternitz
    Pages 223-273

  7. Back Matter

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Keywords

About this book

Many physical phenomena are described by nonlinear evolution equation. Those that are integrable provide various mathematical methods, presented by experts in this tutorial book, to find special analytic solutions to both integrable and partially integrable equations. The direct method to build solutions includes the analysis of singularities à la Painlevé, Lie symmetries leaving the equation invariant, extension of the Hirota method, construction of the nonlinear superposition formula. The main inverse method described here relies on the bi-hamiltonian structure of integrable equations. The book also presents some extension to equations with discrete independent and dependent variables.
The different chapters face from different points of view the theory of exact solutions and of the complete integrability of nonlinear evolution equations. Several examples and applications to concrete problems allow the reader to experience directly the power of the different machineries involved.

Authors, Editors and Affiliations

  • Università di Palermo Dipto. Matematica ed Applicazioni, Palermo, Italy

    Antonio Maria Greco

  • l'Etat Condensé (SPEC), CEA Saclay Service de Physique de, Gif-sur-Yvette CX, France

    Robert M. Conte

  • Università Milano-Bicocca Dipto. Matematica e Applicazioni, Milano, Italy

    Franco Magri

  • Dept. Natuurkunde (DNTK), Vrije Universiteit Brussel Fak. Wetenschappen, Bruxelles, Belgium

    Micheline Musette

  • Mathematical Sciences, University of Tokyo Graduate School of, Tokyo, Japan

    Junkichi Satsuma

  • Université de Montréal Centre de Recherches Mathématiques, Montreal, Canada

    Pavel Winternitz

Bibliographic Information

  • Book Title: Direct and Inverse Methods in Nonlinear Evolution Equations

  • Book Subtitle: Lectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, September 5–12, 1999

  • Authors: Robert M. Conte, Franco Magri, Micheline Musette, Junkichi Satsuma, Pavel Winternitz

  • Editors: Antonio Maria Greco

  • Series Title: Lecture Notes in Physics

  • DOI: https://doi.org/10.1007/b13714

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2003

  • Hardcover ISBN: 978-3-540-20087-1Published: 21 October 2003

  • Softcover ISBN: 978-3-642-05753-3Published: 09 December 2010

  • eBook ISBN: 978-3-540-39808-0Published: 23 September 2003

  • Series ISSN: 0075-8450

  • Series E-ISSN: 1616-6361

  • Edition Number: 1

  • Number of Pages: XI, 279

  • Topics: Mathematical Methods in Physics, Partial Differential Equations, Differential Geometry, Complex Systems, Statistical Physics and Dynamical Systems

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