Perturbation theory for quasiperiodic solutions of infinite-dimensional Hamiltonian systems, and its application to the Korteweg–de Vries equation
Sbornik. Mathematics, Tome 64 (1989) no. 2, pp. 397-413 Cet article a éte moissonné depuis la source Math-Net.Ru

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A perturbation theory is constructed for quasiperiodic solutions of nonlinear conservative systems of large and of infinite dimension. Bibliography: 17 titles.
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S. B. Kuksin. Perturbation theory for quasiperiodic solutions of infinite-dimensional Hamiltonian systems, and its application to the Korteweg–de Vries equation. Sbornik. Mathematics, Tome 64 (1989) no. 2, pp. 397-413. http://geodesic.mathdoc.fr/item/SM_1989_64_2_a7/

[1] Zakharov V. E., “Gamiltonovskii formalizm dlya voln v nelineinykh sredakh s dispersiei”, Radiofizika, 17:4 (1974), 431–453

[2] Dubrovin B. A., Krichever I. M., Novikov S. P., “Integriruemye sistemy”, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 4, VINITI, M., 1985, 179–285 | MR

[3] Zakharov V. E., Manakov S. V., Novikov S. P., Pitaevskii L. P., Teoriya solitonov, ed. S. P. Novikov, Nauka, M., 1980 | MR

[4] Dobrokhotov S. Yu., Maslov V. P., “Multiphase asymptotics of nonlinear partial differential equations with a small parameter”, Math. Phys. Rev., 3 (1982), 221–311 | MR | Zbl

[5] McKean H. P., Trubowitz E., “Hill's operator and hyperelliptic function theory in the presence of infinitely many branch points”, Comm. Pure and Appl. Math., 29 (1976), 143–226 | DOI | MR | Zbl

[6] Krichever I. M., ““Gessiany” integralov uravneniya Kortevega–de Friza i vozmuscheniya konechnozonnykh reshenii”, DAN SSSR, 270:6 (1983), 1312–1317 | MR | Zbl

[7] Kuksin S. B., “Gamiltonovy vozmuscheniya beskonechnomernykh lineinykh sistem s mnimym spektrom”, Funktsion. analiz i ego pril., 21:3 (1987), 22–37 | MR

[8] Kuksin S. B., “Vozmuschenie uslovno-periodicheskikh reshenii beskonechnomernykh gamiltonovykh sistem”, Izv. AN SSSR. Ser. matem., 52 (1988), 41–63 | MR | Zbl

[9] Mozer Yu., “O razlozhenii uslovno-periodicheskikh dvizhenii v skhodyaschiesya stepennye ryady”, UMN, 24:2 (1969), 165–211 | MR

[10] Arnold V. I., Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1974 | MR

[11] Chernoff P. P., Marsden J. E., “Properties of infinite dimensional Hamiltonian systems”, Lect. Notes in Math., 1974, no. 425 | MR

[12] Flaschka H., McLaughlin D. W., “Canonically conjugate variables for Korteweg–de Vries equation and Toda lattice with periodic boundary conditions”, Progress of Theoret. Phys., 55:2 (1976), 438–456 | DOI | MR | Zbl

[13] Lions Zh.-L., Madzhenes E., Neodnorodnye granichnye zadachi i ikh poilozheniya, Mir, M., 1971 | Zbl

[14] Arnold V. I., Givental A. B., “Simplekticheskaya geometriya”, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 4, VINITI, M., 1985, 5–139 | MR

[15] Giiemin V., Sternberg S., Geometricheskie asimptotiki, Mir, M., 1981 | MR

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

[17] Yakupov V. M., “O zadache Koshi dlya uravneniya Kortevega–de Friza”, Differents. uravneniya, 11:3 (1975), 556–561 | Zbl