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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Kupershmidt, Boris A. 1998. Quantum Differential Forms. Journal of Nonlinear Mathematical Physics, Vol. 5, Issue. 3, p. 245.
    der Lende, E.D.van and Pijls, H.G.J. 1990. Super Hamiltonian operators and Lie superalgebras. Indagationes Mathematicae, Vol. 1, Issue. 2, p. 221.
    Kupershmidt, B. A. 1990. A supersymmetric integrable system for arbitrary N. Letters in Mathematical Physics, Vol. 19, Issue. 4, p. 269.
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An algebraic model of graded calculus of variations

  • B. A. Kupershmidt (a1)
Extract

The modern theory of integrable systems rests on two fundamental pillars: the classification of Lax [13] and zero-curvature equations [14, 1, 2]; and algebraic models of the classical calculus of variations [9,5] specialized to the residue calculus in modules of differential forms over rings of matrix pseudo-differential operators [9, 6]. Both these aspects of the theory are by now very well understood for integrable systems in one space dimension.

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COPYRIGHT: © Cambridge Philosophical Society 1987
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[1]Drinfel'd, V. G. and Sokolov., V. V.Korteweg-de Vries equations and simple Lie algebras. Dokl. Akad. Nauk SSSR 258 (1981), 11–16 (Russian); Soviet Math. Dokl. 23 (1981), 457–462 (English).
[2]Drinfel'd, V. G. and Sokolov., V. V.Lie algebras and the Korteweg-de Vries type equations. Itogi Nauki i Tekhniki, ser. Sovremennye Problemi Mathematiki, 24 (1984), 81–180 (Russian); J. Sov. Math. 30 (1985), 1975–2036 (English).
[3]Gel'fand, I. M. and Dikii., L. A.Asymptotic behaviour of the resolvent of Sturm-Liouville equations and the algebra of the Korteweg-de Vries equations. Uspekhi Mat. Nauk (5) 30 (1975), 67–100; Russian Math. Surveys (5) 30 (1975), 77–113.
[4]Kupershmidt., B. A. Geometry of jet bundles and the structures of Lagrangian and Hamiltonian formalisms. Lect. Notes in Math. vol. 775 (Springer-Verlag, 1980), 162–218.
[5]Kupershmidt., B. A.Discrete Lax Equations and Differential-Difference Calculus. Astérisque 123 (1985).
[6]Kupershmidt, B. A. and Wilson., G.Modifying Lax equations and the second Hamiltonian structure. Invent. Math. 62 (1981), 403–436.
[7]Leites., D. A.Introduction to Supermanifolds. Uspekhi Mat. Nauk (1) 35 (1980), 3–57.
[8]Leites., D. A.Theory of Supermanifolds. Petrozavodsk (1983) (in Russian).
[9]Manin., Yu. I.Algebraic aspects of non-linear differential equations. Itogi Nauki i Tekhniki, ser. Sovremennye Problemi Mathematiki 11 (1978), 5–152 (Russian); J. Soviet Math. 11 (1979), 1–122 (English).
[10]Manin, Yu. I.Holomorphic supergeometry and Yang-Mills superfields. Itogi Nauki i Tekhniki, ser. Sovremennye Problemi Mathematiki 24 (1984), 3–180 (in Russian).
[11]Manin, Yu. I. and Radul., A. O.A supersymmetric extension of the Kadomtsev-Petviashvili hierarchy. Comm. Math. Phys. 98 (1985), 65–77.
[12]Rogers., A. Integration of supermanifolds. In Mathematical Aspects of Superspace, ed. Seifert, H–J. et al. (Reidel, D., 1984), pp. 149–160.
[13]Wilson, G., Commuting flows and conservation laws for Lax equations. Math. Proc. Cambridge Philos Soc. 86 (1979), 131–143.
[14]Wilson., G.The modified Lax and two-dimensional Toda lattice equations associated with simple Lie algebras. Erogodic Theory and Dynamical Systems 1 (1981), 361–380.
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
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