Équations différentielles algébriques

Jean-Louis Verdier

Séminaire Bourbaki (1977-1978)

  • Volume: 20, page 101-122
  • ISSN: 0303-1179

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Verdier, Jean-Louis. "Équations différentielles algébriques." Séminaire Bourbaki 20 (1977-1978): 101-122. <http://eudml.org/doc/109912>.

@article{Verdier1977-1978,
author = {Verdier, Jean-Louis},
journal = {Séminaire Bourbaki},
keywords = {algebraic differential equations; Korteweg-de Vries equation; Schrödinger equation; sheaf of differentials},
language = {fre},
pages = {101-122},
publisher = {Springer-Verlag},
title = {Équations différentielles algébriques},
url = {http://eudml.org/doc/109912},
volume = {20},
year = {1977-1978},
}

TY - JOUR
AU - Verdier, Jean-Louis
TI - Équations différentielles algébriques
JO - Séminaire Bourbaki
PY - 1977-1978
PB - Springer-Verlag
VL - 20
SP - 101
EP - 122
LA - fre
KW - algebraic differential equations; Korteweg-de Vries equation; Schrödinger equation; sheaf of differentials
UR - http://eudml.org/doc/109912
ER -

References

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  1. [1] B.A. Dubrovin, I.M. Kričever, S.P. Novikov - The Schrödinger equation in a periodic field and Riemann surfaces, Dokl. Akad. Nauk SSSR, tome 229 (1976), n°1. Translation Soviet Math. Dokl., vol. 17 (1976), n° 4. Zbl0441.35021MR410067
  2. [2] B.A. Dubrovin, V.B. Matveev, S.P. Novikov - Non linear equations of Korteweg-de Vries type, finite zone linear operators, and abelian varieties, Russian Math. Survey, 31:1 (1976), 59-146 from Uspekhi Mat. Nauk, 31:1 (1976), 55-136. Zbl0346.35025MR427869
  3. [3] I.M. Gel'fand, L.A. Dikii - Asymptotic behaviour of the resolvent of Sturm-Liouville equations and the algebra of the Korteweg -de Vries equations, Russian Math. Survey, 30:5 (1975), 77-113 from Uspekhi Mat. Nauk, 30:5 (1975), 67-100. Zbl0334.58007MR508337
  4. [4] I.M. Gel' fand, L.A. Dikii - Fractional powers of operators and Hamiltonian systems, Fonct. Anal. and its Appl., vol. 10, n° 4, oct.-déc. 1976, Transl. April 1977. Zbl0356.35072MR433508
  5. [5] I.M. Kričever - Algebraic-geometric construction of the Zaharov-Sabat equations and their periodic solutions, Dokl. Akad. Nauk SSSR, tome 227 (1976), n°2. Translation Soviet Math. Dokl., vol. 17 (1976), n° 2, 394-397. Zbl0361.35007MR413178
  6. [6] I.M. Kričever - Algebraic curves and commuting matricial differential operators, Fonct. Anal. and it Appl., vol. 10, n° 2, April-June 1976. Zbl0347.35077MR413179
  7. [7] Yu.I. Manin - Aspects algébriques de la théorie des équations différentielles, Itogi Nauki, à paraître. 
  8. [8] V.B. Matveev - Abelian functions and solitons, Instytut Fizyki Teoretycznej, Preprint n° 373, Wroclaw, June 1976. 
  9. [9] H.P. Mckean, E. Trubowitz - Hill's operator and hyperelliptic function theory in the presence of infinitely many branch points, Comm. Pure and Appl. Math., 29 (1976), 143-226. Zbl0339.34024MR427731
  10. [10] H.P. Mckean, P. van Moerbeke - The spectrum of Hill's equation, Inventiones Math., 30 (1975), 217-274. Zbl0319.34024MR397076
  11. [11] D. Mumford - An algebro-geometric construction of commuting operators and of solutions to the Toda lattice equation, Korteweg - de Vries equation and related non linear equations, Proceedings of the Kyoto conference on algebraic geometry, Jan. 1978, à paraître. Zbl0423.14007
  12. [12] S.P. Novikov - Periodic problem for the Korteweg-de Vries equation I, Funktsional'. Analiz i Ego Prilozhen, 9, n° 1, (1975), 65-66. Translation in Funct. Anal., Jan. 1975, 236-246. Zbl0299.35017
  13. [13] J.-L. Burchnall and T.W. Chaundy - Commutative Ordinary differential operators, Proc. London Math. Soc. ser. 2, vol. 21, p. 420-440, (1922). JFM49.0311.03
  14. - Commutative Ordinary differential operators, Proc. Roy. Soc.A, vol. 118, p. 557-583, (1928). Zbl54.0439.01
  15. - Commutative Ordinary Differential operators II - The Identity Pn = Qm , Proc. Roy. Soc.A, vol. 134, p. 471- 485, (1931). 
  16. H.F. Baker, F.R.S. - Note on the Foregoing paper, "Commutative Ordinary Differential Operators", by J.-L. BURCHNALL and J. W. CHAUNDY, Proc. Roy. Soc. A, vol. 118, p. 584-593, (1928). JFM54.0439.02

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