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@article{FAA_1975_9_3_a3, author = {B. A. Dubrovin}, title = {Periodic problems for the {Korteweg--de} {Vries} equation in the class of finite band potentials}, journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a}, pages = {41--51}, publisher = {mathdoc}, volume = {9}, number = {3}, year = {1975}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/FAA_1975_9_3_a3/} }
TY - JOUR AU - B. A. Dubrovin TI - Periodic problems for the Korteweg--de Vries equation in the class of finite band potentials JO - Funkcionalʹnyj analiz i ego priloženiâ PY - 1975 SP - 41 EP - 51 VL - 9 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FAA_1975_9_3_a3/ LA - ru ID - FAA_1975_9_3_a3 ER -
B. A. Dubrovin. Periodic problems for the Korteweg--de Vries equation in the class of finite band potentials. Funkcionalʹnyj analiz i ego priloženiâ, Tome 9 (1975) no. 3, pp. 41-51. http://geodesic.mathdoc.fr/item/FAA_1975_9_3_a3/
[1] Gardner C., Green J., Kruskal M., Miura R., “A method for solving the Korteweg–de Vries equation”, Phys. Rev. Lett., 19 (1967), 1095–1098 | DOI | MR
[2] Lax P., “Integrals of nonlinear equations of evolution and solitary waves”, Comm. Pure Appl. Math., 21:2 (1968), 467–490 | DOI | MR | Zbl
[3] Gelfand I.M., Levitan B.M., “Ob opredelenii differentsialnogo uravneniya po ego spektralnoi funktsii”, Izv. AN SSSR, seriya matem., 15 (1951), 309–360 | MR | Zbl
[4] Marchenko V.A., “Nekotorye voprosy teorii odnomernykh differentsialnykh operatorov. I”, Trudy Mosk. matem. ob-va, I, 1952, 327–420
[5] Faddeev L.D., “Svoistva $S$-matritsy odnomernogo uravneniya Shredingera”, Trudy Matem. in-ta im. V.A. Steklova, LXXIII, 1964, 314–336 | MR
[6] Zakharov V.E., “Kineticheskoe uravnenie dlya solitonov”, ZhETF, 60:3 (1971), 993–1000
[7] Novikov S.P., “Periodicheskaya zadacha dlya uravneniya Kortevega–de Friza. I”, Funkts. analiz, 8:3 (1974), 54–66 | MR | Zbl
[8] Dubrovin B.A., “Obratnaya zadacha teorii rasseyaniya dlya periodicheskikh konechnozonnykh potentsialov”, Funkts. analiz, 9:1 (1975), 65–66 | MR | Zbl
[9] Its A.P., Matveev V.B., “Ob operatorakh Khilla s konechnym chislom lakun”, Funkts. analiz, 9:1 (1975), 69–70 | MR | Zbl
[10] Marchenko V.A., “Periodicheskaya zadacha Kortevega–de Friza”, DAN SSSR, 217:2 (1974), 276–279 | MR | Zbl
[11] Ince E.L., “Further investigations into the periodic Lame functions”, Proc. Roy. Soc. Edinburgh, 60 (1940), 83–99 | DOI | MR
[12] Akhiezer N.I., “Kontinualnyi analog ortogonalnykh mnogochlenov na sisteme intervalov”, DAN SSSR, 141:2 (1961), 263–266 | Zbl
[13] Hochstadt H., “On the determination of a Hill's equation from its spectrum”, Arch. Rat. Mech. and Anal., 19:5 (1965), 353–362 | DOI | MR | Zbl
[14] Titchmarsh E.Ch., Razlozheniya po sobstvennym funktsiyam, svyazannye s differentsialnymi uravneniyami vtorogo poryadka, gl. XXI, v. 2, IL, M., 1961
[15] Shabat A.B., “O potentsialakh s nulevym koeffitsientom otrazheniya”, Dinamika sploshnoi sredy, 5, Novosibirsk, 1970, 130–156
[16] Miura R., Gardner C., Kruskal M., “Kortweg–de Vries equation and generalisations”, J. Math. Phys., 9:8 (1968), 1202–1209 | DOI | MR
[17] 3axarov V.E., Faddeev L.D., “Uravnenie Kortevega–de Friza – vpolne integriruemaya gamiltonova sistema”, Funkts. analiz, 5:4 (1971), 18–27 | MR
[18] 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
[19] Dubrovin B.A., Novikov S.P., “Periodicheskii i uslovno-periodicheskii analogi mnogosolitonnykh reshenii uravneniya KdF”, ZhETF, 12 (1974), 2131–2144 | MR
[20] Lax P., “Periodic solutions of the KdV equations”, Lectures in Appl. Math., 15 (1974), 85–96 | MR