Variational Symplectic Structures

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


A variational symplectic structure on an equation \(\mathcal {E}\) is a \(\mathcal {C}\)-differential operator \(\mathcal {S}\colon \varkappa = \mathcal {F}(\mathcal {E};m)\to \hat {P} = \mathcal {F}(\mathcal {E};r)\) that takes symmetries of \(\mathcal {E}\) to cosymmetries and enjoys additional integrability properties. We expose here the computational theory of local symplectic structures and consider some instructive examples of nonlocal ones. In this chapter we give the solution to Problems  1.22,  1.23, and  1.28.


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© 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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