Algebraic-geometric n-orthogonal curvilinear coordinate systems and solutions of the associativity equations

Functional Analysis and its Applications

Volumn 31, Issue 1, 1997, Pages 25-39

  Krichever, I M ^a  

^a Landau Institute for Theoretical Physics ^*  (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038439840     PISSN: 00162663     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02466001     Document Type: Article

References (17)

1. G. Darboux, Leçons sur le systèmes orthogonaux et les coordonnées curvilignes, Paris, 1910.
2. B. A. Dubrovin and S. P. Novikov, "The Hamiltonian formalism of one-dimensional systems of hydrodynamic type and the Bogolyubov-Whitham averaging method," Dokl. Akad. Nauk SSSR, 27, 665-654 (1983).
3. B. A. Dubrovin and S. P. Novikov, "Hydrodynamics of weakly deformed soliton lattices: Differential geometry and Hamiltonian theory," Usp. Mat. Nauk, 44, 35-124 (1989).
4. S. P. Tsarev, "The geometry of Hamiltonian systems of hydrodynamic type. Generalized hodograph method," Izv. Akad. Nauk SSSR, Ser. Mat., 54, No. 5, 1048-1068 (1990).
5. B. Dubrovin, "Integrable systems in topological field theory," Nuclear Phys. B, 379, 627-689 (1992).
6. I. Krichever, "Tau-function of the universal Whitham hierarchy and topological field theories," Comm. Pure Appl. Math., 47, 1-40 (1994).
7. V. Zakharov, Description of the n-orthogonal curvilinear coordinate systems and hamiltonian integrable systems of hydrodynamic type. Part 1, Integration of the Lamé equations, Preprint (to appear in Duke Math. J.).
8. V. E. Zakharov and S. V. Manakov, Private communication.
9. E. Witten, "The structure of the topological phase of two-dimensional gravity," Nuclear Phys. B, 340, 281-310 (1990).
10. E. Verlinder and H. Verlinder, A solution of two-dimensional topological quantum gravity, Preprint IASSNS-HEP 90/40, PUPT-1176, 1990.
11. I. M. Krichever, "The algebraic-geometric construction of the Zakharov-Shabat equations and their periodic solutions," Dokl. Akad. Nauk SSSR, 227, No. 2, 291-294 (1976).
12. I. M. Krichever, "The integration of nonlinear equations with the help of algebraic-geometric methods," Punkts. Anal. Prilozhen., 11, No. 1, 15-31 (1977).
13. A. R. Its and V. B. Matveev, "On a class of solutions of the Korteweg-de Vries equation," in: Problems of Mathematical Physics, 8, Leningrad State University, 1976.
14. I. Krichever, O. Babelon, E. Billey, and M. Talon, "Spin generalization of the Calogero-Moser system and the matrix KP equation," Am. Math. Soc. Transl. (2), 170, 83-119 (1995).
15. S. P. Novikov and A. P. Veselov, "Finite-gap two-dimensional periodic Schrodinger operators: exact formulas and evolution equations," Dokl. Akad. Nauk SSSR, 279, No. 1, 20-24 (1984).
16. I. M. Krichever, "Algebraic-geometric two-dimensional operators with self-consistent potentials," Funkts. Anal. Prilozhen., 28, No. 1, 26-40 (1994).
17. B. A. Dubrovin, I. M. Krichever, and S. P. Novikov, "The Schrödinger equation in a periodic field and Riemann surfaces," Dokl. Akad. Nauk SSSR, 229, No. 1, 15-18 (1976).