Voir la notice de l'article provenant de la source Math-Net.Ru
@article{FAA_1988_22_2_a0,
author = {A. P. Veselov},
title = {Integrable discrete-time systems and difference operators},
journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
pages = {1--13},
publisher = {mathdoc},
volume = {22},
number = {2},
year = {1988},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FAA_1988_22_2_a0/}
}
A. P. Veselov. Integrable discrete-time systems and difference operators. Funkcionalʹnyj analiz i ego priloženiâ, Tome 22 (1988) no. 2, pp. 1-13. http://geodesic.mathdoc.fr/item/FAA_1988_22_2_a0/
[1] Belobrov P.I., Beloshapkin V.V., Zaslavskii G.M., Tretyakov A.G., “Poryadok i khaos v klassicheskikh modelyakh spinovykh tsepochek”, ZhETF, 87:1 (1984), 310–322
[2] Granovskii Ya.I., Zhedanov A.S., “Periodicheskie struktury na kvantovoi tsepochke spinov”, ZhETF, 89:6 (1985), 2156–2163
[3] Granovskii Ya.I., Zhedanov A.S., “Resheniya domennogo tipa v anizotropnykh magnitnykh tsepochkakh”, TMF, 71:1 (1987), 143–153 | MR
[4] Aubry S., Le Daeron, “The descrete Frenkel–Kontorova model and its extension 1. Exact result for the ground states”, Physica 8D, 1983, 381–422 | MR
[5] Pokrovskii V.L., Khokhlachev S.B., “Neodnorodnye statsionarnye sostoyaniya v modeli Geizenberga”, Pisma v ZhETF, 22:7 (1975), 371–373
[6] Mozer Yu., “Nekotorye aspekty integriruemykh gamiltonovykh sistem”, UMN, 36:5 (1981), 109–151 | MR
[7] Dubrovin B.A., Matveev V.B., Novikov S.P., “Nelineinye uravneniya tipa Kortevega–de Friza, konechnozonnye lineinye operatory i abelevy mnogoobraziya”, UMN, 31:1 (1976), 55–136 | MR | Zbl
[8] Dubrovin B.A., Krichever I.M., Novikov S.P., “Integriruemye sistemy. I”, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya., 4, VINITI, M., 1985, 179–285 | MR | Zbl
[9] Arnold V.I., Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1974 | MR
[10] Bogoyavlenskii O.I., Novikov S.P., “O svyazi gamiltonovykh formalizmov statsionarnykh i nestatsionarnykh zadach”, Funktsion. analiz i ego pril., 10:2 (1976), 9–12 | MR | Zbl
[11] Gelfand I.M., Dikii L.A., “Drobnye stepeni operatorov i gamiltonovy sistemy”, Funktsion. analiz i ego pril., 10:4 (1976), 13–29 | MR
[12] Mokhov O.I., “Gamiltonovost evolyutsionnogo potoka na mnozhestve statsionarnykh tochek ego integrala”, UMN, 39:4 (1984), 173–174 | MR
[13] Veselov A.P., “Uravnenie Landau–Lifshitsa i integriruemye sistemy klassicheskoi mekhaniki”, DAN SSSR, 270:5 (1983), 1094–1097 | MR
[14] Novikov S.P., “Gamiltonov formalizm i mnogoznachnyi analog teorii Morsa”, UMN, 37:5 (1982), 3–49 | DOI | MR | Zbl
[15] Veselov A.P., Geometriya gamiltonovykh sistem, svyazannykh s nelineinymi uravneniyami v chastnykh proizvodnykh, Avtoref. kand. diss., MGU, 1981
[16] Berzhe M., Geometriya, Mir, M., 1984
[17] Griffiths P., Harris J., “On Cayley's explicit solution to Poncelet porism”, Enseign. Math. Ser. 2, 24:1–2 (1978), 31–40 | MR | Zbl
[18] Griffiths P., “Variation on a theme of Abel”, Invent. Math., 35 (1976), 321–390 | DOI | MR | Zbl
[19] Mischenko A.S., “Integraly geodezicheskikh potokov na gruppakh Li”, Funktsion. analiz i ego pril., 4:3 (1970), 73–77 | MR | Zbl
[20] Dikii L.A., “Zamechanie o gamiltonovykh sistemakh, svyazannykh s gruppoi vraschenii”, Funktsion. analiz i ego pril., 6:4 (1972), 83–84 | MR | Zbl
[21] Manakov S.V., “Zamechanie ob integrirovanii uravnenii Eilera dinamiki $n$-mernogo tverdogo tela”, Funktsion. analiz i ego pril., 10:4 (1976), 93–94 | MR | Zbl
[22] Brazovskii S.A., Dzyaloshinskii I.E., Krichever I.M., “Tochno reshaemye diskretnye modeli Paierlsa”, ZhETF, 83:1 (1982), 389–415 | MR
[23] Veselov A.P., Novikov S.P., “Dvumernye potentsialnye operatory Shredingera. Yavnye formuly i evolyutsionnye uravneniya”, DAN SSSR, 275:1 (1984), 20–24 | MR
[24] Veselov A.N., “Konechnozonnye potentsialy i integriruemye sistemy na sfere s kvadratichnym potentsialom”, Funktsion. analiz i ego pril., 14:1 (1980), 48–50 | MR | Zbl
[25] Veselov A.N., “Integrirovanie statsionarnoi zadachi dlya klassicheskoi spinovoi tsepochki”, TMF, 71:1 (1987), 154–159 | MR
[26] Knörrer H., “Geodesic on quadrics and a mechanical problem of C. Neumann”, J. reine angew. Math., 334 (1982), 69–78 | MR | Zbl
[27] Takhtadzhyan L.A., Faddeev L.D., Gamiltonov podkhod v teorii solitonov, Nauka, M., 1986 | MR | Zbl
[28] Ablovitz M., Ladic J., “A non-linear difference scheme and inverse scattering”, Stud. Appl. Math., 55:3 (1976), 213 | DOI | MR
[29] Hirota R., “Non-linear partial difference equations. I–IV”, J. Phys. Soc. Japan, 43 (1977), 1424–1433, 2074-2086 ; 45 (1978), 321–332 | DOI | MR | DOI | MR
[30] Veselov A.N., “Integriruemye otobrazheniya i algebry Li”, DAN SSSR, 292:6 (1987), 1289–1291 | MR | Zbl