no. 3
The theory of differential invariants and KDV hamiltonian evolutions
Bulletin de la Société Mathématique de France, Tome 127 (1999) no. 3, pp. 363-391. 
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     title = {The theory of differential invariants and {KDV} hamiltonian evolutions},
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     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {127},
     number = {3},
     year = {1999},
     doi = {10.24033/bsmf.2353},
     mrnumber = {2001m:37142},
     zbl = {01357366},
     language = {en},
     url = {http://www.numdam.org/articles/10.24033/bsmf.2353/}
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Beffa, Gloria Marí. The theory of differential invariants and KDV hamiltonian evolutions. Bulletin de la Société Mathématique de France, Tome 127 (1999) no. 3, pp. 363-391. doi : 10.24033/bsmf.2353. http://www.numdam.org/articles/10.24033/bsmf.2353/

[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. | MR | Zbl

[2] Drinfel'D (V.G.), Sokolov (V.V.). - Lie algebras and equations of KdV type, J. Soviet Math., t. 30, 1985, p. 1975-2036. | Zbl

[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] González-López (A.), Heredero (R.), Marí Beffa (G.). - Invariant differential equations and the Adler-Gel'fand-Dikii bracket, J. Math. Physics, to appear.

[5] Ince (E.L.). - Ordinary Differential Equations. - Longmans Green, London, 1926. | JFM

[6] Kupershmidt (B.A.), Wilson (G.). - Modifying Lax equations and the second Hamiltonian structure, Inventiones Math., t. 62, 1981, p. 403-36. | MR | Zbl

[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. | MR | Zbl

[8] Marí Beffa (G.), Olver (P.). - Differential Invariants for parametrized projective surfaces, Comm. in Analysis and Geom., to appear. | Zbl

[9] Olver (P.J.). - Applications of Lie Groups to Differential Equations. - Springer-Verlag, New York, 1993. | MR | Zbl

[10] Olver (P.J.). - Equivalence, Invariants, and Symmetry. - Cambridge University Press, Cambridge, 1995. | MR | Zbl

[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] 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. | Zbl

[13] Wilczynski (E.J.). - Projective differential geometry of curves and ruled surfaces. - B.G. Teubner, Leipzig, 1906. | JFM

[14] Wilson (G.). - On the antiplectic pair connected with the Adler-Gel'fand-Dikii bracket, Nonlinearity, t. 50, 1992, p. 109-31. | MR | Zbl

[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. | Zbl

[16] Wilson (G.). - On antiplectic pairs in the Hamiltonian formalism of evolution equations, Quart. J. Math. Oxford, t. 42, 1991, p. 227-256. | MR | Zbl

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