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Volumn 6, Issue 2, 1996, Pages 207-232

On the poisson geometry of the Adler-Gel'fand-Dikii brackets

Author keywords

Adler Gel'fand Dikii brackets; Gelfand Dikii brackets; KdV Hamiltonian structures; Normal forms for ODEs with periodic coefficients; Poisson Geometry; Transverse structures

Indexed keywords


EID: 0041580297     PISSN: 10506926     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02921600     Document Type: Article
Times cited : (7)

References (16)
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  • 3
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    • Normal forms for analytic Poisson structures
    • Conn, J. F. Normal forms for analytic Poisson structures. Ann. of Math. 2(119), 576-601 (1984).
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  • 4
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    • Lie algebras and equations of KdV type
    • Drinfel'd, V. G., and Sokolov, V. V. Lie algebras and equations of KdV type. J. of Sov. Math. 30, 1975-2036 (1985).
    • (1985) J. of Sov. Math. , vol.30 , pp. 1975-2036
    • Drinfel'd, V.G.1    Sokolov, V.V.2
  • 5
    • 8744259713 scopus 로고
    • A family of Hamiltonian structures connected with integrable nonlinear differential equations, in I.M
    • Springer-Verlag
    • Gel'fand, I. M., and Dikii, L. A. A family of Hamiltonian structures connected with integrable nonlinear differential equations, in I.M. Gelfand, Collected Papers, v.1. Springer-Verlag, 1987.
    • (1987) Gelfand, Collected Papers , vol.1
    • Gel'fand, I.M.1    Dikii, L.A.2
  • 7
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    • Integrals of nonlinear equations of evolution and solitary waves
    • Lax, P. D. Integrals of nonlinear equations of evolution and solitary waves. Comm. on Pure and App. Math. 21, 467-490 (1968).
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  • 8
    • 0002680220 scopus 로고
    • Normal forms and versal deformations for Hill's equations
    • Lazutkin, V. F., and Pankratova, T. F. Normal forms and versal deformations for Hill's equations. Funkt. Anal. i Ego Pril. 9(4), 41-48 (1976).
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    • Lazutkin, V.F.1    Pankratova, T.F.2
  • 9
    • 0002449224 scopus 로고
    • A transverse structure for the Lie-Poisson bracket on the dual of the Virasoro algebra
    • Marí Beffa, G. A transverse structure for the Lie-Poisson bracket on the dual of the Virasoro algebra. Pacific J. of Math. 163(1), 43-72 (1994).
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    • Marí Beffa, G.1
  • 10
    • 8744282657 scopus 로고
    • On the Virasoro algebra as a reduced Poisson submanifold of a Kac-Moody algebra
    • Mariacute;' Beffa, G. On the Virasoro algebra as a reduced Poisson submanifold of a Kac-Moody algebra. Proc. of AMS 122(3), 859-869 (1994).
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    • Mariá Beffa, G.1
  • 11
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    • Reduction of Poisson manifolds
    • Marsden, J., and Ratiu, T. Reduction of Poisson manifolds. Lett. in Math. Phys. 11, 161-169 (1986).
    • (1986) Lett. in Math. Phys. , vol.11 , pp. 161-169
    • Marsden, J.1    Ratiu, T.2
  • 12
    • 34249916116 scopus 로고
    • Symplectic leaves of the Gelfand-Dikii brackets and homotopy classes of nondegenerate curves
    • Ovsienko, V. Yu., and Khesin, B. A. Symplectic leaves of the Gelfand-Dikii brackets and homotopy classes of nondegenerate curves, Fukt. Anal. i Ego Prol. 24(1), 38-47 (1990) or Fund. Anal. Appl. 24 (1990).
    • (1990) Fukt. Anal. I Ego Prol. , vol.24 , Issue.1 , pp. 38-47
    • Ovsienko, V.Yu.1    Khesin, B.A.2
  • 13
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    • Ovsienko, V. Yu., and Khesin, B. A. Symplectic leaves of the Gelfand-Dikii brackets and homotopy classes of nondegenerate curves, Fukt. Anal. i Ego Prol. 24(1), 38-47 (1990) or Fund. Anal. Appl. 24 (1990).
    • (1990) Fund. Anal. Appl. , vol.24
  • 15
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    • Current algebras and nonlinear partial differential equations
    • Reiman, A. G., and Semenov-Tjan-Sanskii, M. A. Current algebras and nonlinear partial differential equations. Sov. Math. Dokl. 21, 2 (1980).
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    • Reiman, A.G.1    Semenov-Tjan-Sanskii, M.A.2
  • 16
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    • The local structure of Poisson manifolds
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    • Weinstein, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.