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2000 | 51 | 1 | 187-196
Tytuł artykułu

The Theory of differential invariance and infinite dimensional Hamiltonian evolutions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we describe the close relationship between invariant evolutions of projective curves and the Hamiltonian evolutions of Adler, Gel'fand and Dikii. We also show how KdV evolutions are related as well to invariant evolutions of projective surfaces.
Słowa kluczowe
Rocznik
Tom
51
Numer
1
Strony
187-196
Opis fizyczny
Daty
wydano
2000
Twórcy
  • Department of Mathematics, University of Wisconsin, Madison, WI 53706, U.S.A.
Bibliografia
  • [1] M. Adler, On a Trace Functional for Formal Pseudo-differential Operators and the Symplectic Structure of the KdV, Inventiones Math. 50 (1979), 219-248.
  • [2] V. G. Drinfel'd and V. V. Sokolov, Lie Algebras and Equations of KdV Type, J. of Sov. Math. 30 (1985), 1975-2036.
  • [3] M. Fels and P. J. Olver Moving coframes. I. A practical algorithm, Acta Appl. Math. 51 (1998), 161-213.
  • [4] M. Fels and P. J. Olver Moving coframes. II. Regularization and theoretical foundations, Acta Appl. Math. 55 (1999), 127-208.
  • [5] I. M. Gel'fand and L. A. Dikii, A family of Hamiltonian structures connected with integrable nonlinear differential equations, in: I. M. Gelfand, Collected papers v.1, Springer-Verlag, 1987.
  • [6] A. González-López, R. Hernandez and G. Marí Beffa, Invariant differential equations and the Adler-Gel'fand-Dikii bracket, J. Math. Phys. 38 (1997), 5720-5738.
  • [7] B. A. Kupershmidt and G. Wilson, Modifying Lax equations and the second Hamiltonian structure, Inventiones Math. 62 (1981), 403-436.
  • [8] G. Marí Beffa, Differential invariants and KdV Hamiltonian evolutions, Bull. Soc. Math. France 127 (1999) 363-391.
  • [9] G. Marí Beffa and P. Olver, Differential Invariants for parametrized projective surfaces, Comm. Anal. Geom. 7 (1999), 807-839.
  • [10] P. Olver, Equivalence, Invariants and Symmetries, Cambridge University Press, Cambridge (1995).
  • [11] I. McIntosh, SL(n+1)-invariant equations which reduce to equations of Korteweg-de Vries type, Proc. of the Royal Soc. of Edinburgh 115A (1990), 367-381.
  • [12] E. J. Wilczynski, Projective differential geometry of curves and ruled surfaces, B.G. Teubner, Leipzig (1906).
  • [13] G. Wilson, On the antiplectic pair connected with the Adler-Gel'fand-Dikii bracket, Nonlinearity 5 (1992), 109-31.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv51z1p187bwm
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