The laplace method, algebraic curves, and nonlinear equations

I. M. Krichever

Funkcionalʹnyj analiz i ego priloženiâ, Tome 18 (1984) no. 3, pp. 43-56.

Bibliographie

[1] Novikov S.P., “Dvumernye operatory Shredingera v periodicheskikh polyakh”, Sovremennye problemy matematiki (Itogi nauki i tekhniki), 23, VINITI AN SSSR, M., 1983, 3–32 | MR

[2] Calogero F., Degasperis A., “Inverse spectral problem for the one-dimensional Schroedinger equation with an additional linear potential”, Lett. Nuovo Cimento, 23 (1978), 143–149 | DOI | MR

[3] Calogero F., Degasperis A., “Solution by the spectral transform method of a nonlinear evolution equation including as a special case the cylindrical KdV equation”, Lett. Nuovo Cimento, 23 (1978), 150–154 | DOI | MR

[4] Calodgero F., Degasperis A., Spectral transform and solitions: tools to solve and investigate nonlinear evolution equations, North-Holland Pub. Com., Amsterdam–New York–Oxford, 1982 | MR

[5] Li Yishen, “One special inverse problem of the second order differential equation on the whole real axis”, Chin. Ann. Math, 2 (1981), 147–156 | MR | Zbl

[6] Graffi S., Harrell E., “Inverse scattering for one-dimensional Stare effect and application to the cylindrical KdV equation”, Ann. Inst. Henri Poincare, 36 (1982), 41–58 | MR | Zbl

[7] Gursa E., Kurs matematicheskogo analiza, T. 2, ONTI, M., 1936

[8] 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

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

[10] Krichever I.M., “Metody algebraicheskoi geometrii v teorii nelineinykh uravnenii”, UMN, 32:6 (1977), 183–208 | MR | Zbl

[11] Krichever I.M., Novikov S.P., “Golomorfnye rassloeniya nad algebraicheskimi krivymi i nelineinye uravneniya”, UMN, 35:6 (1980), 47–68 | MR | Zbl

[12] Dubrovin B.A., “Teta-funktsii i nelineinye uravneniya”, UMN, 36:2 (1981), 11–80 | MR | Zbl

[13] Dubrovin B.A., Krichever I.M., Novikov S.P., “Topological and algebraic geometry methods in contemporary mathematical physics II”, Soviet Scientific Reviews. Mathematical Phys. Reviews, 3, OPA, Amsterdam, 1982 | MR

[14] Krichever I.M., “Nelineinye uravneniya i ellipticheskie krivye”, Sovremennye problemy matematiki (Itogi nauki i tekhniki), 23, VINITI AN SSSR, M., 1983, 79–136 | MR

[15] Dubrovin B.A., “Matrichnye konechnozonnye operatory”, Sovremennye problemy matematiki (Itogi nauki i tekhniki), 23, VINITI AN SSSR, M., 1983, 33–78 | MR

[16] Krichever I.M., Novikov S.P., “Golomorfnye rassloeniya nad rimanovymi poverkhnostyami i uravnenie Kadomtseva–Petviashvili I”, Funkts. analiz, 12:4 (1978), 41–52 | MR | Zbl

[17] Krichever I.M., Novikov S.P., “Golomorfnye rassloeniya i nelineinye uravneniya. Konechnozonnye resheniya ranga 2”, DAN SSSR, 247:1 (1979), 33–37 | MR | Zbl

[18] Zakharov V.E., Shabat A.B., “Skhema integrirovaniya nelineinykh uravnenii matematicheskoi fiziki metodom obratnoi zadachi teorii rasseyaniya 1”, Funkts. analiz, 8:3 (1974), 43–53 | MR | Zbl

[19] Krichever I.M., “Algebro-geometricheskoe postroenie uravnenii Zakharova–Shabata i ikh periodicheskikh reshenii”, DAN SSSR, 227:2 (1976), 291–294 | MR | Zbl

[20] Krichever I.M., “Integrirovanie nelineinykh uravnenii metodami algebraicheskoi geometrii”, Funkts. analiz, 11:1 (1977), 15–31 | MR | Zbl

[21] Springer Dzh., Vvedenie v teoriyu rimanovykh poverkhnostei, IL, M., 1961

[22] Cherednik I.V., “Ob usloviyakh veschestvennosti v ”, DAN SSSR, 252:5 (1980), 1104–1108 | MR | Zbl

[23] Krichever I.M., “Analog formuly Dalambera dlya uravnenii glavnogo kiralnogo polya i uravneniya sine-gordon”, DAN SSSR, 253:2 (1980), 288–292 | MR | Zbl

[24] Leznov A.N., Saveliev M.N., “On the two-dimensional system differential equations”, Comm. Math. Phys., 74 (1980), 111–119 | DOI | MR

[25] Mansfild P., Solutions of Toda lattice, Preprint Cambridge Univ. Cambridge, CB 39 EW, 1982

[26] Mikhailov A.V., “Ob integriruemosti dvumernogo obobscheniya tsepochki Toda”, Pisma v ZhETF, 30 (1978), 443–448

[27] Date E., Tanaka S., “Exact solutions for the periodic Toda lattice”, Prog. Theor. Phys., 53 (1976), 267–273 | MR

[28] Krichever I.M., “Algebraicheskie krivye i nelineinye raznostnye uravneniya”, UMN, 33:4 (1978), 215–216 | MR | Zbl

[29] Its A.R., Matveev V.B., “Ob odnom klasse reshenii uravneniya Kortevega–de Friza”, Problemy matem. fiziki, 8, Izd. LGU, L., 1978

[30] Fay J., Theta-functions on Riemann surfaces, Lect. Notes in Math., 352, 1973 | DOI | MR | Zbl

[31] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, Nauka, M., 1974

[32] Landau L. D., Lifshits E.M., Kvantovaya mekhanika (nerelyativistskaya teoriya), Nauka, M., 1974 | MR

[33] Maslov V.P., Operatornye metody, Nauka, M., 1973 | MR

[34] Manakov S.V., “O polnoi integriruemosti i stokhastizatsii v diskretnykh dinamicheskikh sistemakh”, ZhETF, 67:2 (1974), 543–555 | MR

[35] Krichever I.M., “Algebro-geometricheskaya spektralnaya teoriya raznostnogo operatora Shredingera i model Paierlsa”, DAN SSSR, 265:5 (1982), 1054–1058 | MR | Zbl

[36] Bordag L.A., Matveev V.B., Darboux transformation and explicit solutions of the cylindrical KdV, Preprint LPTH E No 6, Leipzig, 1979 | MR

[37] Dryuma V.S., “Analiticheskie resheniya aksialno-simmetricheskogo uravneniya KdF”, Izv. AN Mold.SSR, 3 (1976), 297–301