On the formalism of local variational differential operators

S. Igonin, A.V. Verbovetsky, R. Vitolo

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    Abstract

    The calculus of local variational differential operators introduced by B. L. Voronov, I. V. Tyutin, and Sh. S. Shakhverdiev is studied in the context of jet super space geometry. In a coordinate-free way, we relate these operators to variational multivectors, for which we introduce and compute the variational Poisson and Schouten brackets by means of a unifying algebraic scheme. We give a geometric definition of the algebra of multilocal functionals and prove that local variational differential operators are well defined on this algebra. To achieve this, we obtain some analytical results on the calculus of variations in smooth vector bundles, which may be of independent interest. In addition, our results give a new a new efficient method for finding Hamiltonian structures of differential equations.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Publication statusPublished - 2002

    Publication series

    Name
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1641
    ISSN (Print)0169-2690

    Keywords

    • MSC-58J70
    • MSC-37K05
    • MSC-81T70
    • MSC-35A30
    • IR-65827
    • EWI-3461

    Cite this

    Igonin, S., Verbovetsky, A. V., & Vitolo, R. (2002). On the formalism of local variational differential operators. Enschede: University of Twente, Department of Applied Mathematics.