Geodesic
On the Hamiltonian property of an arbitrary evolution system on the set of stationary points of its integral
Izvestiya. Mathematics , Tome 31 (1988) no. 3, pp. 657-664.

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The Bogoyavlenskii–Novikov principle concerning the connection between stationary and nonstationary problems is generalized. It is proved that an arbitrary evolution system is Hamiltonian on the set of stationary points of its local integral. Bibliography: 16 titles. 
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O. I. Mokhov. On the Hamiltonian property of an arbitrary evolution system on the set of stationary points of its integral. Izvestiya. Mathematics , Tome 31 (1988) no. 3, pp. 657-664. http://geodesic.mathdoc.fr/item/IM2_1988_31_3_a10/

[1] Novikov S. P., “Periodicheskaya zadacha Kortevega–de Friza”, Funkts. analiz i ego prilozh., 8 (1974), 54–66 | MR | Zbl

[2] Bogoyavlenskii O. I., Novikov S. P., “O svyazi gamiltonovykh formalizmov statsionarnykh i nestatsionarnykh zadach”, Funkts. analiz i ego prilozh., 10:1 (1976), 9–13 | MR | Zbl

[3] Dubrovin B. A., Matveev V. B., Novikov S. P., “Nelineinye uravneniya tipa Kortevega–de Friza, konechnozonnye lineinye operatory i abelevy mnogoobraziya”, Uspekhi matem. nauk, 31:1 (1976), 55–136 | MR | Zbl

[4] Zakharov V. E., Manakov S. V., Novikov S. P., Pitaevskii L. P., Teoriya solitonov: metod obratnoi zadachi, Nauka, M., 1980 | MR

[5] Gelfand I. M., Dikii L. A., “Drobnye stepeni operatorov i gamiltonovy sistemy”, Funkts. analiz i ego prilozh., 10:4 (1976), 13–29 | MR

[6] Gelfand I. M., Dikii L. A., “Rezolventa i gamiltonovy sistemy”, Funkts. analiz i ego prilozh., 11:2 (1977), 11–27 | MR

[7] Veselov A. P., “O gamiltonovom formalizme dlya uravnenii Novikova–Krichevera kommutativnosti dvukh operatorov”, Funkts. analiz i ego prilozh., 13:1 (1979), 1–7 | MR | Zbl

[8] Gelfand I. M., Manin Yu. I., Shubin M. A., “Skobki Puassona i yadro variatsionnoi proizvodnoi v formalnom variatsionnom ischislenii”, Funkts. analiz i ego prilozh., 10:4 (1976), 30–34 | MR

[9] Manin Yu. I., “Algebraicheskie aspekty nelineinykh differentsialnykh uravnenii”, Itogi nauki i tekhniki. Sovremennye problemy matematiki, 11, VINITI, 1978, 5–152 | MR

[10] Mokhov O. I., “Gamiltonovost evolyutsionnogo potoka na mnozhestve statsionarnykh tochek ego integrala”, Uspekhi matem. nauk, 39:4 (1984), 173–174 | MR | Zbl

[11] Lax P. D., “Periodic solutions of the KdV equation”, Lectures in Appl. Math., 15, 1974, 85–96 | MR

[12] Dubrovin B. A., Novikov S. P., Fomenko A. T., Sovremennaya geometriya: metody i prilozheniya, Nauka, M., 1986 | MR

[13] Gelfand I. M., Dorfman I. Ya., “Gamiltonovy operatory i svyazannye s nimi algebraicheskie struktury”, Funkts. analiz i ego prilozh., 13:4 (1979), 13–30 | MR

[14] Magri F., “A simple model of the integrable Hamiltonian equation”, Math. Phys., 19:5 (1978), 1156–1162 | DOI | MR | Zbl

[15] Mokhov O. I., “Lokalnye skobki Puassona tretego poryadka”, Uspekhi matem. nauk, 40:5 (1985), 257–258 | MR | Zbl

[16] Kupershmidt B. A., Wilson G., “Modifying Lax equations and the second hamiltonian structure”, Invent Math., 62:3 (1981), 403–436 | DOI | MR