References
S. V. Manakov, “A remark about the integration of Euler equations for the dynamics of an n-dimensional rigid body,” Funkts. Anal. Prilozh.,10, No. 4, 93–94 (1976).
A. M. Perelomov, “Some remarks about the integration of equations of motion for a rigid body in ideal fluid,” Funkts. Anal. Prilozh.,15, No. 2, 83–85 (1981).
A. I. Bobenko, “Euler equations on the algebras e(3) and so(4). Isomorphism of integrable cases,” Funkts. Anal. Prilozh.,20, No. 1, 64–66 (1986).
A. V. Bolsinov, “Liouville integrable Hamiltonian systems on Lie algebras,” Dissertation, Candidacy in Mathematical Physics, Moscow State University, Moscow (1987).
B. Kostant, “The solution to generalized Toda lattice and representation theory,” Adv. Math.,34, No. 3, 195–338 (1979).
A. Clebsch, “Ueber die Bewegung eines Körpers in einer Flüssigkeit,” Math. Ann., No. 3, 238–262 (1870).
F. Brun, “Rotation krix fix punkt,” Uvers. Konigl. Svensca. Vetenk. Akad. Vorhandl, Stockholm, No. 7, 455–468.
C. Neumann, “De probleme quodam mechanico, quod ad primam integralium ultra-ellipticoram classem revocatum,” J. Reine Angew. Math., No. 56, 46–63 (1859).
A. Gurvitz and R. Kurant, Function Theory [in Russian], Nauka, Moscow (1968).
M. Adler and P. van Moerbeke, “Geodesic flows on so(4) and intersections of quadrics,” Proc. Natl. Acad. Sci. USA,81, 4613–4616 (1984).
L. Heine, “Geodesic flows on so(4) and abelian surfaces,” Math. Ann.,263, 435–472 (1983).
E. K. Sklyanin and A. E. Borovik, “On the integrability of the Landau—Lifshits equation,” Preprint LOMI E-3-79, Leningrad (1979).
A. P. Veselov, “The Landau—Lifshits equation and integrable systems of classical mechanics,” Dokl. Akad. Nauk SSSR,270, No. 5, 1094–1097 (1983).
E. Kotter, “Uber die Bewegung eines festen Körpers in einer Flüssigkeit I, II,” J. Reine Angewandte Math.,109, 51–81, 89–111 (1892).
B. A. Dubrovin, S. P. Novikov, and I. M. Krichever, “Integrable systems,” Itogi Nauki Tekh., Modern Problems in Mathematics,4, 179–285 (1985).
V. Volterra, “Sur la théorie des variations des latitudes,” Acta Math.,22, 201–357 (1899).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 54, No. 1, pp. 94–109, July, 1993.
The author would like to express deep gratitude to B. A. Dubrovin for stimulating discussions.
Rights and permissions
About this article
Cite this article
Fedorov, Y.N. Lax representations with a spectral parameter defined on coverings of hyperelliptic curves. Math Notes 54, 728–738 (1993). https://doi.org/10.1007/BF01224367
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01224367