Advertisement

The Tangent Covering

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

Abstract

The tangent covering is an equation naturally related to the initial equation \(\mathbb {E}\) and which covers the latter and plays the same role in the category of differential equations that the tangent bundle plays in the category of smooth manifolds. It is used to construct recursion operators for symmetries of \(\mathbb {E}\) and symplectic structures on \(\mathbb {E}\). In this chapter we give the solution to Problem  1.18 and also prepare a basis to solution of Problems  1.20 (Chap.  7) and  1.22 (Chap.  8).

References

  1. 74.
    Krasilshchik, I.S., Kersten, P.H.M.: Symmetries and Recursion Operators for Classical and Supersymmetric Differential Equations. Kluwer, Dordrecht/Boston (2000)Google Scholar
  2. 82.
    Krasilshchik, J., Verbovetsky, A.M.: Geometry of jet spaces and integrable systems. J. Geom. Phys. 61, 1633–1674 (2011). arXiv:1002.0077Google Scholar
  3. 84.
    Leites, D.A.: Introduction to the theory of supermanifolds. Russ. Math. Surv. 35(1), 1–64 (1980)MathSciNetCrossRefzbMATHGoogle Scholar

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

Personalised recommendations