×

Polynomial integrals of dynamical systems and the Lax reduction. (English. Russian original) Zbl 0915.58039

Math. Notes 61, No. 3, 363-365 (1997); translation from Mat. Zametki 61, No. 3, 445-446 (1997).
The author considers partial differential equations of so-called hydrodynamic type. It is proved the hydrodynamical integrability of such equations.

MSC:

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.)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] E. T. Whittaker,A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, Cambridge Univ. Press, Cambridge (1937). · JFM 63.1286.03
[2] G. D. Birkhoff,Dynamical Systems Colloquium Publ., Vol. 9, Amer. Math. Soc. (1927).
[3] V. V. Kozlov,Mat. Zametki [Math. Notes],45, No. 4, 46–52 (1989).
[4] B. A. Dubrovin and S. P. Novikov,Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],270, No. 4, 781–785 (1983).
[5] S. P. Tsarev,Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],282, No. 3, 534–537 (1985).
[6] Y. Kodama and J. Gibbons,Phys. Lett. A.,135, No. 3, 167–170 (1989).
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.