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@article{FAA_1977_11_1_a2,
author = {I. M. Krichever},
title = {Integration of nonlinear equations by the methods of algebraic geometry},
journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
pages = {15--31},
publisher = {mathdoc},
volume = {11},
number = {1},
year = {1977},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FAA_1977_11_1_a2/}
}
I. M. Krichever. Integration of nonlinear equations by the methods of algebraic geometry. Funkcionalʹnyj analiz i ego priloženiâ, Tome 11 (1977) no. 1, pp. 15-31. http://geodesic.mathdoc.fr/item/FAA_1977_11_1_a2/
[1] Cardner C., Green J., Kruskal M., Miura R., “Method for solving the Korteweg–de Vries equation”, Phys. Rev. Lett., 19 (1967), 1095–1098 | DOI | MR
[2] Zakharov V.E., Shabat A.V., “Skhema integrirovaniya nelineinykh uravnenii matematicheskoi fiziki metodom obratnoi zadachi rasseyaniya. I”, Funkts. analiz, 8:3 (1974), 43–53 | MR | Zbl
[3] Dubrovin B.A., Matveev V.V., Novikov S.P., “Nelineinye uravneniya tipa Kortevega–de Friza, konechnozonnye lineinye operatory i abelevy mnogoobraziya”, UMN, XXXI:1 (1976), 55–136 | MR
[4] Krichever I.M., “Algebro-geometricheskoe postroenie uravnenii Zakharova–Shabata i ikh periodicheskikh reshenii”, DAN SSSR, 227:2 (1976), 291–294 | MR | Zbl
[5] Krichever I.M., “Algebraicheskie krivye i kommutiruyuschie matrichnye differentsialnye operatory”, Funkts. analiz, 10:2 (1976), 75–76 | MR
[6] Dubrovin B.A., Krichever I.M., Novikov S.P., “Uravnenie Shredingera v periodicheskom pole i rimanovy poverkhnosti”, DAN SSSR, 229:1 (1976), 15–19 | MR
[7] Novikov S.P., “Periodicheskaya zadacha dlya uravneniya Kortevega–de Friza. ”, Funkts. analiz, 8:3 (1974), 54–66 | MR | Zbl
[8] Gelfand I.M., Dikii L.A., “Asimptotika rezolventy shturm-liuvillevskikh operatorov i algebra uravnenii Kortevega–de Friza”, UMN, XXX:5 (1975), 67–100 | MR
[9] Bogoyavlenskii O.I., “Ob integralakh vysshikh statsionarnykh uravnenii KdF i sobstvennykh chislakh operatora Khilla”, Funkts. analiz, 10:2 (1976), 9–12 | MR | Zbl
[10] Shafarevich I.R., Osnovy algebraicheskoi geometrii, Nauka, M., 1972 | MR | Zbl
[11] Krichever I.M., “Bezotrazhatelnye potentsialy na fone konechnozonnykh”, Funkts. analiz, 9:2 (1975), 77–78 | MR | Zbl
[12] Springer Dzh., Vvedenie v teoriyu rimanovykh poverkhnostei, IL, M., 1961
[13] Akhiezer N.I., “Kontinualnyi analog ortogonalnykh mnogochlenov na sisteme intervalov”, DAN SSSR, 141:2 (1961), 263–266 | Zbl
[14] Dubrovin B.A., “Periodicheskaya zadacha dlya uravneniya Kortevega–de Friza v klasse konechnozonnykh potentsialov”, Funkts. analiz, 9:3 (1975), 41–51 | MR | Zbl
[15] Its A.R., Matveev V.B., “Operatory Shredingera s konechnozonnym spektrom i $N$-solitonnye resheniya uravneniya Kortevega–de Friza”, Teor. i matem. fizika, 23:1 (1975), 51–68 | MR
[16] Dubrovin B.A., Novikov S.P., “Periodicheskaya zadacha dlya uravneniya Kortevega–de Friza i Shturma–Liuvillya. Ikh svyaz s algebraicheskoi geometriei”, DAN SSSR, 219:3 (1974), 19–22 | MR
[17] Chebotarev N.G., Teoriya algebraicheskikh funktsii, Gostekhizdat, M., 1948
[18] Zverovich E.I., “Kraevye zadachi teorii analiticheskikh funktsii v gelderovskikh klassakh na rimanovykh poverkhnostyakh”, UMN, XXVI:1 (1971), 113–179 | MR
[19] Its A.R., Matveev V.B., “Ob odnom klasse reshenii uravneniya KdF”, Problemy matematicheskoi fiziki, 8, LGU, 1976
[20] Kadomtsev B.V., Petviashvili V.I., “Ob ustoichivosti uedinennykh voln v slabo dispergiruyuschikh sredakh”, DAN SSSR, 192:4 (1970), 753–756 | Zbl
[21] Zakharov V.E., “K probleme stokhastizatsii odnomernykh tsepochek nelineinykh ostsillyatorov”, ZhETF, 65:1 (1973), 219–225
[22] Bogoyavlensky O.I., On perturbations of the Toda lattice, preprint, Chernogolovka, 1976 | MR
[23] Lax P.D., “Periodic solutions of the KdV equations”, Comm. Pure Appl. Math., 28 (1975), 141–188 | DOI | MR | Zbl
[24] Gelfand I.M., Dikii L.A., “Drobnye stepeni operatorov i gamiltonovy sistemy”, Funkts. analiz, 10:4 (1976), 13–29 | MR