The theory of differential invariants and KDV hamiltonian evolutions

Gloria Marí Beffa

Bulletin de la Société Mathématique de France (1999)

  • Volume: 127, Issue: 3, page 363-391
  • ISSN: 0037-9484

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Beffa, Gloria Marí. "The theory of differential invariants and KDV hamiltonian evolutions." Bulletin de la Société Mathématique de France 127.3 (1999): 363-391. <http://eudml.org/doc/87811>.

@article{Beffa1999,
author = {Beffa, Gloria Marí},
journal = {Bulletin de la Société Mathématique de France},
keywords = {differential invariants; projective action; invariant evolutions of projective curves; KdV Hamiltonian evolutions; Adler-Gel'fand-Dikii Poisson brackets},
language = {eng},
number = {3},
pages = {363-391},
publisher = {Société mathématique de France},
title = {The theory of differential invariants and KDV hamiltonian evolutions},
url = {http://eudml.org/doc/87811},
volume = {127},
year = {1999},
}

TY - JOUR
AU - Beffa, Gloria Marí
TI - The theory of differential invariants and KDV hamiltonian evolutions
JO - Bulletin de la Société Mathématique de France
PY - 1999
PB - Société mathématique de France
VL - 127
IS - 3
SP - 363
EP - 391
LA - eng
KW - differential invariants; projective action; invariant evolutions of projective curves; KdV Hamiltonian evolutions; Adler-Gel'fand-Dikii Poisson brackets
UR - http://eudml.org/doc/87811
ER -

References

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  1. [1] ADLER (M.). — On a trace functional for formal pseudo-differential operators and the symplectic structure of the KdV, Inventiones Math., t. 50, 1979, p. 219-48. Zbl0393.35058MR80i:58026
  2. [2] DRINFEL'D (V.G.), SOKOLOV (V.V.). — Lie algebras and equations of KdV type, J. Soviet Math., t. 30, 1985, p. 1975-2036. Zbl0578.58040
  3. [3] GEL'FAND (I.M.), DIKII (L.A.). — A family of Hamiltonian structures connected with integrable nonlinear differential equations. — I.M. Gel'fand collected papers I, Springer-Verlag, New York, 1987. 
  4. [4] GONZÁLEZ-LÓPEZ (A.), HEREDERO (R.), MARÍ BEFFA (G.). — Invariant differential equations and the Adler-Gel'fand-Dikii bracket, J. Math. Physics, to appear. Zbl0892.58037
  5. [5] INCE (E.L.). — Ordinary Differential Equations. — Longmans Green, London, 1926. Zbl0063.02971JFM53.0399.07
  6. [6] KUPERSHMIDT (B.A.), WILSON (G.). — Modifying Lax equations and the second Hamiltonian structure, Inventiones Math., t. 62, 1981, p. 403-36. Zbl0464.35024MR84m:58055
  7. [7] MCINTOSH (I.). — SL(n + 1)-invariant equations which reduce to equations of Korteweg-de Vries type, Proc. Royal Soc. Edinburgh, t. 115A, 1990, p. 367-81. Zbl0724.35095MR91i:58063
  8. [8] MARÍ BEFFA (G.), OLVER (P.). — Differential Invariants for parametrized projective surfaces, Comm. in Analysis and Geom., to appear. Zbl0949.53012
  9. [9] OLVER (P.J.). — Applications of Lie Groups to Differential Equations. — Springer-Verlag, New York, 1993. Zbl0785.58003MR94g:58260
  10. [10] OLVER (P.J.). — Equivalence, Invariants, and Symmetry. — Cambridge University Press, Cambridge, 1995. Zbl0837.58001MR96i:58005
  11. [11] OLVER (P.J.), SAPIRO (G.), TANNENBAUM (A.). — Differential invariant signatures and flows in computer vision : a symmetry group approach, Geometry-Driven Diffusion in Computer Vision. — B.M. ter Haar Romeny, ed., Kluwer Acad. Publ., Dordrecht, The Netherlands, 1994. 
  12. [12] OVSIENKO (V. Yu.), KHESIN (B.A.). — Symplectic leaves of the Gelfand-Dikii brackets and homotopy classes of nondegenerate curves, Funct. Anal. Appl., t. 24, 1990, p. 38-47. Zbl0723.58021
  13. [13] WILCZYNSKI (E.J.). — Projective differential geometry of curves and ruled surfaces. — B.G. Teubner, Leipzig, 1906. Zbl37.0620.02JFM37.0620.02
  14. [14] WILSON (G.). — On the antiplectic pair connected with the Adler-Gel'fand-Dikii bracket, Nonlinearity, t. 50, 1992, p. 109-31. Zbl0761.58023MR93b:58083
  15. [15] WILSON (G.). — On the Adler-Gel'fand-Dikii bracket, Hamiltonian systems, transformation groups and spectral transform methods. — Proc. CRM Workshop, eds : Harnad and Marsden, 1989. Zbl0737.35111
  16. [16] WILSON (G.). — On antiplectic pairs in the Hamiltonian formalism of evolution equations, Quart. J. Math. Oxford, t. 42, 1991, p. 227-256. Zbl0755.58030MR92j:58054

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