Computational Problems and Dedicated Software

  • Joseph Krasil’shchik
  • Alexander Verbovetsky
  • Raffaele Vitolo
Part of the Texts & Monographs in Symbolic Computation book series (TEXTSMONOGR)


In this chapter, we give an overview of the basic computational problems that arise in the study of geometrical aspects related to nonlinear partial differential equations and in the study of their integrability in particular.

We also discuss the historical development and the latest features of the Reduce software that we will use to solve the above computational problems: CDIFF, developed around 1990 by our colleagues P.K.H. Gragert, P.H.M. Kersten, G.F. Post, and G.H.M. Roelofs of the University of Twente and the CDE package, developed by one of us (RV).

Finally, we review other publicly available software that is currently used in similar computational tasks.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

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

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