Spectral theory of finite-zone nonstationary Schr\"odinger operators. A nonstationary Peierls model

I. M. Krichever

Funkcionalʹnyj analiz i ego priloženiâ, Tome 20 (1986) no. 3, pp. 42-54.

Bibliographie

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

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

[3] 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

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

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

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

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

[8] Dubrovin B.A., Krichever I.M., Novikov S.P., “Topological and algebraic geometry methods in contemporary mathematical physics. II”, Soviet Scientific Reviews. Math. Phys. Reviews, 3, OPA, Amsterdam, 1982, 1–151 | MR

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

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

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

[12] Brazovspii S.A., Gordyunin S.A., Kirova N.N., “Tochnoe reshenie modeli Paierlsa s proizvolnym chislom elektronov na elementarnuyu yacheiku”, Pisma v ZhETF, 31:8 (1980), 486–490

[13] Belokolos E.D., “Zadachi Paierlsa-Frelikha i konechnozonnye potentsialy. I”, TMF, 45:2 (1980), 268–275 | MR

[14] Belokolos E.D., “Zadachi Paierlsa-Frelikha i konechnozonnye potentsialy. II”, TMF, 48:1 (1981), 60–69 | MR

[15] Brazovskii S.A., Dzyaloshinskii I.E., Krichever I.M., “Tochno reshaemye diskretnye modeli Paierlsa”, ZhETF, 83:1 (1982), 389–415 | MR

[16] Dzyaloshinskii I.E., Krichever I.M., “Zvuk i volna zaryadovoi plotnosti v diskretnoi modeli Paierlsa”, ZhETF, 85:11 (1983), 1771–1789

[17] Krichever I.M., “Model Paierlsa”, Funktsion. analiz i ego pril., 16:4 (1982), 10–26 | MR

[18] Dzyaloshinskii I.E., Krichever I.M., “Effekty soizmerimosti v diskretnoi modeli Paierlsa”, ZhETF, 83:5 (1982), 1576–1581 | MR

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

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

[21] Krichever I.M., “O ratsionalnykh resheniyakh uravneniya Kadomtseva–Petviashvili i ob integriruemykh sistemakh chastits na pryamoi”, Fukntsion. analiz i ego pril., 12:1 (1978), 76–78 | MR | Zbl

[22] Bordag L.A., Its A.R., Matveev V.B., Manakov S.F., Zakharov V.E., “Two-dimensional solitons of Kadomtzev–Petviashvely equation”, Phys. Lett., 1977, 205–207

[23] Krichever I.M., “Metod Laplasa, algebraicheskie krivye i nelineinye uravneniya”, Funktsion. analiz i ego pril., 18:3 (1984), 43–56 | MR | Zbl

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

[25] Matveev V.B., “Darboux transformations and the solutions of KP equation depending: on the functional parameters”, Lect. Math. Phys., 3 (1979), 213–225 | DOI | MR

[26] Kuznetsov E.A., Mikhailov A.B., “Ustoichivost statsionarnykh voln v nelineinykh sredakh so slaboi dispersiei”, ZhETF, 67:11 (1974), 1019–1027

[27] Dubrovin B.A., “Periodicheskaya zadacha dlya uravneniya Kortevega–de Friza”, Funktsion. analiz i ego pril., 9:3 (1975), 41–51 | MR | Zbl

[28] Dubrovin B.A., “Obratnaya zadacha rasseyaniya dlya periodicheskikh konechnozonnykh potentsialov”, Funktsion. analiz i ego pril., 9:1 (1975), 65–66 | MR | Zbl

[29] Cherednik I.V., “Differentsialnye uravneniya dlya funktsii Beikera–Akhiezera”, Funktsion. analiz i ego pril., 12:3 (1978), 45–54 | MR | Zbl

[30] Yajima N., Oikawa M., “Interections between langmure's and sonice waves”, Prog. Theor. Phys., 56 (1976), 17–19 | DOI | MR

[31] Makchankov V.G., “On the stationary solutions of Schrodinger equation with self-congruent potential satisfi Bussinesque equation”, Phys. Lett., 50, A. (1974), 42–44. | DOI

[32] Bogomolov Y., Kol'chugina I., Litvak A., Sergeev A., “Near-sonic Langmur solitons”, Phys. Lett., 91A (1982), 9–14

[33] Melnikov V.K., “Nekotorye novye nelineinye evolyutsionnye uravneniya, integriruemye metodom obratnoi zadachi”, Mat. sb., 121:4 (1983), 469–498 | MR

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

[35] Date E., Jimbo M., Kashivara, Miva T., “Transformation groups for solitonequations I.”, Proc. Japan Acad., 57A (1981), 342–347 | MR