The D-Boussinesq equation: Hamiltonian and symplectic structures; Noether and inverse Noether operators

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

    Research output: Book/ReportReportProfessional

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    Abstract

    Using new methods of analysis of integrable systems,based on a general geometric approach to nonlinear PDE,we discuss the Dispersionless Boussinesq Equation, which is equivalent to the Benney-Lax equation,being a system of equations of hydrodynamical type. The results include: a description of local and nonlocal Hamiltonian and symplectic structures, hierarchies of symmetries, hierarchies of conservation laws, recursion operators for symmetries and generating functions of conservation laws. Highly interesting are the appearences of the Noether and Inverse Noether operators ,leading to multiple infinite hierarchies of these operators as well as recursion operators.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    ISBN (Print)0169-2690
    Publication statusPublished - 2005

    Publication series

    NameTW-Memorandum
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1752
    ISSN (Print)0169-2690

    Keywords

    • MSC-35Q53
    • MSC-37K05
    • METIS-227112
    • EWI-3572
    • IR-65936

    Cite this

    Verbovetsky, A. V., Verbovetsky, A., Kersten, P. H. M., & Krasil'shchik, I. (2005). The D-Boussinesq equation: Hamiltonian and symplectic structures; Noether and inverse Noether operators. (TW-Memorandum; No. 1752). Enschede: University of Twente, Department of Applied Mathematics.
    Verbovetsky, A.V. ; Verbovetsky, A. ; Kersten, P.H.M. ; Krasil'shchik, I. / The D-Boussinesq equation: Hamiltonian and symplectic structures; Noether and inverse Noether operators. Enschede : University of Twente, Department of Applied Mathematics, 2005. (TW-Memorandum; 1752).
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    title = "The D-Boussinesq equation: Hamiltonian and symplectic structures; Noether and inverse Noether operators",
    abstract = "Using new methods of analysis of integrable systems,based on a general geometric approach to nonlinear PDE,we discuss the Dispersionless Boussinesq Equation, which is equivalent to the Benney-Lax equation,being a system of equations of hydrodynamical type. The results include: a description of local and nonlocal Hamiltonian and symplectic structures, hierarchies of symmetries, hierarchies of conservation laws, recursion operators for symmetries and generating functions of conservation laws. Highly interesting are the appearences of the Noether and Inverse Noether operators ,leading to multiple infinite hierarchies of these operators as well as recursion operators.",
    keywords = "MSC-35Q53, MSC-37K05, METIS-227112, EWI-3572, IR-65936",
    author = "A.V. Verbovetsky and A. Verbovetsky and P.H.M. Kersten and I. Krasil'shchik",
    note = "Imported from MEMORANDA",
    year = "2005",
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    Verbovetsky, AV, Verbovetsky, A, Kersten, PHM & Krasil'shchik, I 2005, The D-Boussinesq equation: Hamiltonian and symplectic structures; Noether and inverse Noether operators. TW-Memorandum, no. 1752, University of Twente, Department of Applied Mathematics, Enschede.

    The D-Boussinesq equation: Hamiltonian and symplectic structures; Noether and inverse Noether operators. / Verbovetsky, A.V.; Verbovetsky, A.; Kersten, P.H.M.; Krasil'shchik, I.

    Enschede : University of Twente, Department of Applied Mathematics, 2005. (TW-Memorandum; No. 1752).

    Research output: Book/ReportReportProfessional

    TY - BOOK

    T1 - The D-Boussinesq equation: Hamiltonian and symplectic structures; Noether and inverse Noether operators

    AU - Verbovetsky, A.V.

    AU - Verbovetsky, A.

    AU - Kersten, P.H.M.

    AU - Krasil'shchik, I.

    N1 - Imported from MEMORANDA

    PY - 2005

    Y1 - 2005

    N2 - Using new methods of analysis of integrable systems,based on a general geometric approach to nonlinear PDE,we discuss the Dispersionless Boussinesq Equation, which is equivalent to the Benney-Lax equation,being a system of equations of hydrodynamical type. The results include: a description of local and nonlocal Hamiltonian and symplectic structures, hierarchies of symmetries, hierarchies of conservation laws, recursion operators for symmetries and generating functions of conservation laws. Highly interesting are the appearences of the Noether and Inverse Noether operators ,leading to multiple infinite hierarchies of these operators as well as recursion operators.

    AB - Using new methods of analysis of integrable systems,based on a general geometric approach to nonlinear PDE,we discuss the Dispersionless Boussinesq Equation, which is equivalent to the Benney-Lax equation,being a system of equations of hydrodynamical type. The results include: a description of local and nonlocal Hamiltonian and symplectic structures, hierarchies of symmetries, hierarchies of conservation laws, recursion operators for symmetries and generating functions of conservation laws. Highly interesting are the appearences of the Noether and Inverse Noether operators ,leading to multiple infinite hierarchies of these operators as well as recursion operators.

    KW - MSC-35Q53

    KW - MSC-37K05

    KW - METIS-227112

    KW - EWI-3572

    KW - IR-65936

    M3 - Report

    SN - 0169-2690

    T3 - TW-Memorandum

    BT - The D-Boussinesq equation: Hamiltonian and symplectic structures; Noether and inverse Noether operators

    PB - University of Twente, Department of Applied Mathematics

    CY - Enschede

    ER -

    Verbovetsky AV, Verbovetsky A, Kersten PHM, Krasil'shchik I. The D-Boussinesq equation: Hamiltonian and symplectic structures; Noether and inverse Noether operators. Enschede: University of Twente, Department of Applied Mathematics, 2005. (TW-Memorandum; 1752).