Complete integrability of dynamical systems generated by singular solutions of Liouville’s equation. (English) Zbl 0461.35083


35Q99 Partial differential equations of mathematical physics and other areas of application
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)


Zbl 0451.35084
Full Text: DOI


[1] L. D. Faddeev, in: Modern Problems of Mathematics [in Russian], Itogi nauki i tekhniki, VINITI,3, 93 (1974).
[2] V. E. Zakharov, L. A. Takhtadzhyan, and L. D. Faddeev, Dokl. Akad. Nauk SSR,219, 1334 (1974).
[3] L. A. Takhtadzhyan and L. D. Faddeev, Teor. Mat. Fiz.,21, 160 (1974).
[4] G. P. Jorjadze, A. K. Pogrebkov, and M. C. Polivanov, Preprint IC/78/126, Trieste (1978).
[5] A. K. Pogrebkov, Dokl. Akad. Nauk SSSR,244, 873 (1979).
[6] G. P. Dzhordzhadze, A. K. Pogrebkov, and M. K. Polivanov, Teor. Mat. Fiz.,40, 221 (1979).
[7] J. Liouville, J. Math. Pure Appl.,18, 71 (1853).
[8] L. T. Todorov, Preprint E2-10125 [in English], JINR, Dubna (1976); V. V. Molotkov and I. T. Todorov, Preprint E2-12270 [in English], JINR, Dubna (1979).
[9] S. N. Sokolov, Preprint IFVÉ, OTF 78-125 [in Russian], Serpukhov (1978).
[10] Lo-Keng Hua, Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains, American Mathematical Society Translations of Mathematical Monographs, Vol. 6 (1963).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.