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  • © 2017

The Symbolic Computation of Integrability Structures for Partial Differential Equations

  • Proposes a new approach and new software for computations
  • Discusses example programs
  • Represents the only book on integrable systems and symbolic computations of integrability operators

Part of the book series: Texts & Monographs in Symbolic Computation (TEXTSMONOGR)

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Softcover Book USD 119.99
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Hardcover Book USD 119.99
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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xv
  2. Computational Problems and Dedicated Software

    • Joseph Krasil’shchik, Alexander Verbovetsky, Raffaele Vitolo
    Pages 1-26
  3. Internal Coordinates and Total Derivatives

    • Joseph Krasil’shchik, Alexander Verbovetsky, Raffaele Vitolo
    Pages 27-57
  4. Conservation Laws and Nonlocal Variables

    • Joseph Krasil’shchik, Alexander Verbovetsky, Raffaele Vitolo
    Pages 59-85
  5. Cosymmetries

    • Joseph Krasil’shchik, Alexander Verbovetsky, Raffaele Vitolo
    Pages 87-103
  6. Symmetries

    • Joseph Krasil’shchik, Alexander Verbovetsky, Raffaele Vitolo
    Pages 105-132
  7. The Tangent Covering

    • Joseph Krasil’shchik, Alexander Verbovetsky, Raffaele Vitolo
    Pages 133-148
  8. Recursion Operators for Symmetries

    • Joseph Krasil’shchik, Alexander Verbovetsky, Raffaele Vitolo
    Pages 149-168
  9. Variational Symplectic Structures

    • Joseph Krasil’shchik, Alexander Verbovetsky, Raffaele Vitolo
    Pages 169-184
  10. Cotangent Covering

    • Joseph Krasil’shchik, Alexander Verbovetsky, Raffaele Vitolo
    Pages 185-192
  11. Variational Poisson Structures

    • Joseph Krasil’shchik, Alexander Verbovetsky, Raffaele Vitolo
    Pages 193-214
  12. Recursion Operators for Cosymmetries

    • Joseph Krasil’shchik, Alexander Verbovetsky, Raffaele Vitolo
    Pages 215-224
  13. Back Matter

    Pages 225-263

About this book

This is the first book devoted to the task of computing integrability structures by computer. The symbolic computation of integrability operator is a computationally hard problem and the book covers a huge number of situations through tutorials. The mathematical part of the book is a new approach to integrability structures that allows to treat all of them in a unified way. The software is an official package of Reduce. Reduce is free software, so everybody can download it and make experiments using the programs available at our website.

Authors and Affiliations

  • V.A. Trapeznikov Institute of Control Sciences RAS, Independent University of Moscow, Moscow, Russia

    Joseph Krasil'shchik

  • Independent University of Moscow, Moscow, Russia

    Alexander Verbovetsky

  • Department of Mathematics and Physics ‘E. De Giorgi’, University of Salento, Lecce, Italy

    Raffaele Vitolo

About the authors

Joseph Krasil'shchik is a principal researcher at the Institute of Control Sciences of Russian Academy of Sciences and a full professor at the Independent University of Moscow. 

Alexander Verbovetsky is a lecturer at the Independent University of Moscow. 

Raffaele Vitolo is an associate professor in mathematical physics at the Department of Mathematics and Physics ‘E. De Giorgi’ of the Università del Salento.

Bibliographic Information

Buy it now

Buying options

eBook USD 89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 119.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access