Algebraic-Geometric $n$-Orthogonal Curvilinear Coordinate Systems and Solutions of the Associativity Equations
Funkcionalʹnyj analiz i ego priloženiâ, Tome 31 (1997) no. 1, pp. 32-50.

Voir la notice de l'article provenant de la source Math-Net.Ru

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I. M. Krichever. Algebraic-Geometric $n$-Orthogonal Curvilinear Coordinate Systems and Solutions of the Associativity Equations. Funkcionalʹnyj analiz i ego priloženiâ, Tome 31 (1997) no. 1, pp. 32-50. http://geodesic.mathdoc.fr/item/FAA_1997_31_1_a3/

[1] Darboux G., Lecons sur le systems ortogonaux et les coordones curvilignes, Paris, 1910

[2] Dubrovin B. A., Novikov S. P., “Gamiltonov formalizm odnomernykh sistem gidrodinamicheskogo tipa i metod usredneniya Bogolyubova–Uizema”, DAN SSSR, 27 (1983), 665–654

[3] Dubrovin B. A., Novikov S. P., “Gidrodinamika slabo deformirovannykh solitonnykh reshetok: Differentsialnaya geometriya i gamiltonova teoriya”, UMN, 44 (1989), 35–124 | MR | Zbl

[4] Tsarev S. P., “Geometriya gamiltonovykh sistem gidrodinamicheskogo tipa. Obobschennyi metod godografa”, Izv. AN SSSR, ser. matem., 54:5 (1990), 1048–1068 | MR | Zbl

[5] Dubrovin B., “Integrable systems in topological field theory”, Nuclear Phys. B, 379 (1992), 627–689 | DOI | MR

[6] Krichever I., “Tau-function of the universal Whitham hierarchy and topological field theories”, Comm. Pure Appl. Math., 47 (1994), 1–40 | DOI | MR

[7] Zakharov V., Description of the $n$-ortogonal curvilinear coordinate systems and hamiltonian integrable systems of hydrodynamic type. Part 1. Integration of the Lamé equations, Preprint, Duke Math. J. (to appear) | MR

[8] Zakharov V. E., Manakov S. V., Chastnoe soobschenie

[9] Witten E., “The structure of the topological phase of two-dimensional gravity”, Nuclear Phys. B, 340 (1990), 281–310 | DOI | MR

[10] Verlinder E., Verlinder H., A solution of two-dimensional topological quantim gravity, Preprint IASSNS-HEP 90/40, PUPT-1176, 1990 | MR

[11] Krichever I. M., “Algebro-geometricheskaya konstruktsiya uravnenii Zakharova–Shabata i ikh periodicheskikh reshenii”, DAN SSSR, 227:2 (1976), 291–294 | MR | Zbl

[12] Krichever I. M., “Integrirovanie nelineinykh uravnenii metodami algebraicheskoi geometrii”, Funkts. analiz i ego pril., 11:1 (1977), 15–31 | MR | Zbl

[13] Its A. R., Matveev V. B., Ob odnom klasse reshenii uravneniya KdF, Problemy matematicheskoi fiziki, 8, LGU, 1976

[14] Krichever I., Babelon O., Billey E., Talon M., “Spin generalization of the Calogero–Moser system and the matrix KP equation”, Am. Math. Soc. Transl. (2), 170, Amer. Math. Soc., Providence, RI, 1995, 83–119 | MR | Zbl

[15] Veselov A. P., Novikov S. P., “Konechnozonnye dvumernye periodicheskie operatory Shredingera: yavnye formuly i evolyutsionnye uravneniya”, DAN SSSR, 279:1 (1984), 20–24 | MR | Zbl

[16] Krichever I. M., “Algebro-geometricheskie dvumernye operatory s samosoglasovannymi potentsialami”, Funkts. analiz i ego pril., 28:1 (1994), 26–40 | MR | Zbl

[17] Dubrovin B. A., Krichever I. M., Novikov S. P., “Uravnenie Shredingera v magnitnom pole i rimanovy poverkhnosti”, DAN SSSR, 229:1 (1976), 15–18 | MR | Zbl