Recursion Operators for Cosymmetries

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

Abstract

These \(\mathcal {C}\)-differential operators are somewhat dual (see Remark 11.1 below) to recursion operators for symmetries considered in Sect.  7. They send cosymmetries of an equation \(\mathcal {E}\) to themselves. (Actually, recursion operators for cosymmetries take solutions of the equation \(\tilde {\ell }_{\mathcal {E}}^*(\psi )=0\) in some covering over \(\mathcal {E}\), i.e. shadows of cosymmetries, to objects of the same nature.) Though these operators are not so popular in applications as their symmetry counterparts, we expose briefly our approach to compute them. In this chapter we give the solution to Problems  1.27 and  1.28.

References

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    Kersten, P., Krasilshchik, I., Verbovetsky, A.: A geometric study of the dispersionless Boussinesq type equation. Acta Appl. Math. 90, 143–178 (2006)Google Scholar
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    Sheftel, M.B., Yazıcı, D.: Bi-Hamiltonian representation, symmetries and integrals of mixed heavenly and Husain systems. J. Nonlinear Math. Phys. 7(4), 453–484 (2010). arXiv:0904.3981Google 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

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