M. A. Olshanetsky, A. M. Perelomov, “The Toda chain as a reduced system”, TMF, 45:1 (1980), 3–18; Theoret. and Math. Phys., 45:1 (1980), 843

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Teoreticheskaya i Matematicheskaya Fizika, 1980, Volume 45, Number 1, Pages 3–18 (Mi tmf3761)

This article is cited in 15 scientific papers (total in 15 papers)

The Toda chain as a reduced system

M. A. Olshanetsky, A. M. Perelomov

Full-text PDF (1959 kB) Citations (15)

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Abstract: It is proved that the phase space of a finite Toda chain can be obtained by means of the reduction of the phase space of a geodesic flow on the uniform space of symmetric positive-definite matrices. The reduction is performed with the aid of the group of triangular matrices and makes it possible to obtain explicit formulas for solutions of the equations of motion. The construction is extended to the generalised Toda chains corresponding to an arbitrary system of roots.

Received: 26.08.1979

English version:
Theoretical and Mathematical Physics, 1980, Volume 45, Issue 1, Pages 843–854
DOI: https://doi.org/10.1007/BF01047139

Bibliographic databases:

Language: Russian

Citation: M. A. Olshanetsky, A. M. Perelomov, “The Toda chain as a reduced system”, TMF, 45:1 (1980), 3–18; Theoret. and Math. Phys., 45:1 (1980), 843–854

Citation in format AMSBIB

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\jour Theoret. and Math. Phys.

\yr 1980

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https://www.mathnet.ru/eng/tmf3761

https://www.mathnet.ru/eng/tmf/v45/i1/p3

This publication is cited in the following 15 articles:

Anatoly Dymarsky, Alexander Gorsky, “Quantum chaos as delocalization in Krylov space”, Phys. Rev. B, 102:8 (2020)
A. V. Marshakov, A. D. Mironov, A. Yu. Morozov, “Combinatorial expansions of conformal blocks”, Theoret. and Math. Phys., 164:1 (2010), 831–852
V.S. Gerdjikov, G. Vilasi, A.B. Yanovski, Lecture Notes in Physics, 748, Integrable Hamiltonian Hierarchies, 2008, 175
V.S. Gerdjikov, G. Vilasi, A.B. Yanovski, Lecture Notes in Physics, 748, Integrable Hamiltonian Hierarchies, 2008, 211
V.S. Gerdjikov, G. Vilasi, A.B. Yanovski, Lecture Notes in Physics, 748, Integrable Hamiltonian Hierarchies, 2008, 315
Luiz A. Ferreira, Erica E. Leite, “Integrable theories in any dimension and homogenous spaces”, Nuclear Physics B, 547:3 (1999), 471
A. D. Mironov, “Group theory approach to the $\tau$ -function and its quantization”, Theoret. and Math. Phys., 114:2 (1998), 127–183
László Fehér, Izumi Tsutsui, “Regularization of Toda lattices by Hamiltonian reduction”, Journal of Geometry and Physics, 21:2 (1997), 97
Theoret. and Math. Phys., 103:3 (1995), 681–700
L.A. Ferreira, J.Luis Miramontes, Joaquín Sánchez Guillén, “Solitons, τ-functions and hamiltonian reduction for non-Abelian conformal affine Toda theories”, Nuclear Physics B, 449:3 (1995), 631
C.P. Constantinidis, L.A. Ferreira, J.F. Gomes, A.H. Zimerman, “Connection between the affine and conformal affine Toda models and their Hirota solution”, Physics Letters B, 298:1-2 (1993), 88
H. Aratyn, L.A. Ferreira, J.F. Gomes, A.H. Zimerman, “Kac-Moody construction of Toda type field theories”, Physics Letters B, 254:3-4 (1991), 372
L. A. Ferreira, R. M. Londe, “Solutions to higher Hamiltonians in the Toda hierarchies”, Journal of Mathematical Physics, 31:12 (1990), 3041
A. Yu. Daletskii, G. B. Podkolzin, “A group approach to the integration of the infinite Toda chain”, Ukr Math J, 40:4 (1989), 445
Yu. K. Mozer, “Nekotorye aspekty integriruemykh gamiltonovykh sistem”, UMN, 36:5(221) (1981), 109–151

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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