The Monge-Ampère equation: Hamiltonian and symplectic structures, recursions, and hierarchies

P.H.M. Kersten, I. Krasil'shchik, A.V. Verbovetsky

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    Abstract

    Using methods of geometry and cohomology developed recently, we study the Monge-Ampère equation, arising as the first nontrivial equation in the associativity equations, or WDVV equations. We describe Hamiltonian and symplectic structures as well as recursion operators for this equation in its orginal form, thus treating the independent variables on an equal footing. Besides this we present nonlocal symmetries and generating functions (cosymmetries).
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Publication statusPublished - 2004

    Publication series

    Name
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1727
    ISSN (Print)0169-2690

    Keywords

    • MSC-35Q53
    • MSC-37K05
    • EWI-3547
    • Hamiltonian structure
    • Monge-Ampère equation
    • IR-65911
    • Recursion operator
    • associativity equations
    • conservation law
    • symplectic structure
    • Symmetry

    Cite this

    Kersten, P. H. M., Krasil'shchik, I., & Verbovetsky, A. V. (2004). The Monge-Ampère equation: Hamiltonian and symplectic structures, recursions, and hierarchies. Enschede: University of Twente, Department of Applied Mathematics.