Advertisement

The Symbolic Computation of Integrability Structures for Partial Differential Equations

  • Joseph Krasil'shchik
  • Alexander Verbovetsky
  • Raffaele Vitolo

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

Table of contents

  1. Front Matter
    Pages i-xv
  2. Joseph Krasil’shchik, Alexander Verbovetsky, Raffaele Vitolo
    Pages 1-26
  3. Joseph Krasil’shchik, Alexander Verbovetsky, Raffaele Vitolo
    Pages 27-57
  4. Joseph Krasil’shchik, Alexander Verbovetsky, Raffaele Vitolo
    Pages 59-85
  5. Joseph Krasil’shchik, Alexander Verbovetsky, Raffaele Vitolo
    Pages 87-103
  6. Joseph Krasil’shchik, Alexander Verbovetsky, Raffaele Vitolo
    Pages 105-132
  7. Joseph Krasil’shchik, Alexander Verbovetsky, Raffaele Vitolo
    Pages 133-148
  8. Joseph Krasil’shchik, Alexander Verbovetsky, Raffaele Vitolo
    Pages 149-168
  9. Joseph Krasil’shchik, Alexander Verbovetsky, Raffaele Vitolo
    Pages 169-184
  10. Joseph Krasil’shchik, Alexander Verbovetsky, Raffaele Vitolo
    Pages 185-192
  11. Joseph Krasil’shchik, Alexander Verbovetsky, Raffaele Vitolo
    Pages 193-214
  12. Joseph Krasil’shchik, Alexander Verbovetsky, Raffaele Vitolo
    Pages 215-224
  13. Back Matter
    Pages 225-263

About this book

Introduction

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.

Keywords

integrable systems Hamiltonian operators Symplectic operators Recursion operators geometry of jet spaces

Authors and affiliations

  • Joseph Krasil'shchik
    • 1
  • Alexander Verbovetsky
    • 2
  • Raffaele Vitolo
    • 3
  1. 1.V.A. Trapeznikov Institute of Control Sciences RASIndependent University of MoscowMoscowRussia
  2. 2.Independent University of MoscowMoscowRussia
  3. 3.Department of Mathematics and Physics ‘E. De Giorgi’University of SalentoLecceItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-71655-8
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2017
  • Publisher Name Springer, Cham
  • eBook Packages Computer Science
  • Print ISBN 978-3-319-71654-1
  • Online ISBN 978-3-319-71655-8
  • Series Print ISSN 0943-853X
  • Series Online ISSN 2197-8409
  • Buy this book on publisher's site