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MR ZblDubrovin, Boris. On analytic families of invariant tori for PDES, dans Analyse complexe, systèmes dynamiques, sommabilité des séries divergentes et théories galoisiennes (II), Astérisque, no. 297 (2004), pp. 35-65. http://geodesic.mathdoc.fr/item/AST_2004__297__35_0/
@incollection{AST_2004__297__35_0,
author = {Dubrovin, Boris},
title = {On analytic families of invariant tori for {PDES}},
booktitle = {Analyse complexe, syst\`emes dynamiques, sommabilit\'e des s\'eries divergentes et th\'eories galoisiennes (II)},
editor = {Loday-Richaud Mich\`ele},
series = {Ast\'erisque},
pages = {35--65},
year = {2004},
publisher = {Soci\'et\'e math\'ematique de France},
number = {297},
mrnumber = {2135674},
zbl = {1087.35083},
language = {en},
url = {http://geodesic.mathdoc.fr/item/AST_2004__297__35_0/}
}
TY - CHAP AU - Dubrovin, Boris TI - On analytic families of invariant tori for PDES BT - Analyse complexe, systèmes dynamiques, sommabilité des séries divergentes et théories galoisiennes (II) AU - Collectif ED - Loday-Richaud Michèle T3 - Astérisque PY - 2004 SP - 35 EP - 65 IS - 297 PB - Société mathématique de France UR - http://geodesic.mathdoc.fr/item/AST_2004__297__35_0/ LA - en ID - AST_2004__297__35_0 ER -
%0 Book Section %A Dubrovin, Boris %T On analytic families of invariant tori for PDES %B Analyse complexe, systèmes dynamiques, sommabilité des séries divergentes et théories galoisiennes (II) %A Collectif %E Loday-Richaud Michèle %S Astérisque %D 2004 %P 35-65 %N 297 %I Société mathématique de France %U http://geodesic.mathdoc.fr/item/AST_2004__297__35_0/ %G en %F AST_2004__297__35_0
[1] & - Riemann Surfaces, Princeton Mathematical Series, vol. 26, Princeton University Press, Princeton, N.J., 1960. | MR | Zbl
[2] - Mathematical Methods of Classical Mechanics, Springer-Verlag, New York, NY, 1978. | MR | Zbl | DOI
[3] , , , & - Algebro- Geometric Approach to Nonlinear Integrable Equations, Springer-Verlag, NY, 1994. | Zbl
[4] & - "Periodic multiphase solutions of the Kadomsev-Petviashvili equation", J. Phys. A 22 (1989), p. 1259-1274. | MR | Zbl | DOI
[5] , , & - "Density of heat curves in the moduli space", in Panoramas of mathematics (Warsaw, 1992/1994), Banach Center Publ., vol. 34, Polish Acad. Sci., Warsaw, 1995, p. 19-27. | MR | Zbl | EuDML
[6] - "On the Cauchy problem for the Kadomtsev-Petviashvili equation", Geom. Funct. Anal. 3 (1993), p. 315-341. | MR | Zbl | EuDML | DOI
[7] - Problèmes de petits diviseurs dans les équations aux dérivées partielles, Panoramas & Synthèses, vol. 9, Société Mathématique de France, Paris, 2000. | MR | Zbl
[8] - "On S.P. Novikov's conjecture in the theory of v-functions and nonlinear equations of Korteweg-de Vries and Kadomcev-Petviasvili type", Dokl. Akad. Nauk SSSR 251 (1980), no. 3, p. 541-544. | MR | Zbl
[9] , "The Kadomtsev-Petviashvili equation and relations between periods of holomorphic differentials on Riemann surfaces". Izv. Akad. Nauk SSSR Ser. Mat. 45 (1981), no. 5, p. 1015-1028, 1198. | MR | Zbl
[10] , "Theta functions and nonlinear equations", Russian Math. Surveys 36 (1981), p. 11-92. | Zbl | MR | DOI
[11] , & - "Three-phase solutions of the Kadomtsev- Petviashvili equation", Stud. Appl. Math. 99 (1997), p. 137-203. | MR | Zbl | DOI
[12] , & - "Nonlinear equations of Korteweg-de Vries type, finite-band linear operators and Abelian varieties", Russian Math. Surveys 31 (1976), p. 59-146. | Zbl | MR | DOI
[13] & - "Real theta-function solutions of the Kadomtsev- Petviashvili equation", Izv. Akad. Nauk SSSR Ser. Mat. 52 (1988), no. 2, p. 267-286, | MR | Zbl
& - "Real theta-function solutions of the Kadomtsev- Petviashvili equation", translation in Math. USSR-Izv. 32 (1989), p. 269-288. | MR | Zbl | DOI
[14] - "Zum Quantensatz von Sommerfeld und Epstein", Deutsche Physikalische Gesellschaft, Verhandlungen 19 (1917), p. 82-92.
[15] - "Hamiltonian systems with Poisson commuting integrals", Ph.D. Thesis, KTH Stockholm, 1984.
[16] - Theta Functions on Riemann Surfaces, Lect. Notes in Math., vol. 352, Springer-Verlag, Berlin-Heidelberg-New York, 1973. | MR | Zbl
[17] , & - Riemann Surfaces of Infinite Genus, CRM Monograph Series, vol. 20, American Mathematical Society, Providence, RI, 2003. | MR | Zbl | DOI
[18] & - Principles of Algebraic Geometry, Pure and Applied Mathematics, Wiley-Interscience (John Wiley & Sons), New York, 1978. | MR | Zbl
[19] , , & - "Two-dimensional periodic waves in shallow water. II. Asymmetric waves", J. Fluid Mech. 285 (1995), p. 95-122. | MR | DOI
[20] , & - "Two-dimensional periodic waves in shallow water", J. Fluid Mech. 209 (1989), p. 567-589. | MR | DOI
[21] - "Convergence of Birkhoff normal forms for integrable systems", Comment. Math. Helv. 64 (1989), p. 412-461. | MR | Zbl | EuDML | DOI
[22] , "Integrability of Hamiltonian systems and Birkhoff normal forms in the simple resonance case", Math. Ann. 292 (1992), p. 411-444. | MR | Zbl | EuDML | DOI
[23] & - "On the stability of solitary waves in a weakly dispersing medium", Soviet. Phys. Dokl. 15 (1970), p. 539-541. | Zbl
[24] & - KdV & KAM, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, vol. 45, Springer-Verlag, Berlin, 2003. | MR | Zbl
[25] - "Algebrogeometric construction of the Zakharov-Shabat equations and their periodic solutions", Dokl. Akad. Nauk SSSR 227 (1976), p. 291-294. | Zbl | MR
[26] , "Methods of algebraic geometry in the theory of nonlinear equations", Russian Math. Surveys 32 (1977), p. 185-213. | Zbl | DOI
[27] , "Spectral theory of two-dimensional periodic operators and its applications", Uspekhi Mat. Nauk 44 (1989), no. 2, p. 121-184, | MR | Zbl
, "Spectral theory of two-dimensional periodic operators and its applications", translation in Russian Math. Surveys 44 (1989), p. 145-225. | MR | Zbl | DOI
[28] - Nearly Integrable Infinite-Dimensional Hamiltonian Systems, Lect. Notes in Math., vol. 155, Springer-Verlag, Berlin, 1993. | MR | Zbl
[29] , & - Statistical physics. Pt.1. 3rd ed., Course of theoretical physics, vol. 5, Pergamon, London, 1980. | Zbl
[30] & - "The small dispersion limit of the Korteweg-de Vries equation I. II. III", Comm. Pure Appl. Math. 36 (1983), p. 253-290; 571-593; 809-829. | MR | Zbl | DOI
[31] & - "Hill's operator and hyperelliptic function theory in the presence of infinitely many branch points", Comm. Pure Appl. Math. 29 (1976), p. 143-226. | MR | Zbl | DOI
[32] - "A direct method of calculating periodic wave solutions to nonlinear evolution equations. I. Exact two-periodic wave solution", J. Phys. Soc. Japan, 47 (1979), p. 1701-1705. | MR | Zbl | DOI
[33] , , & - Theory of solitons. The inverse scattering method. Consultants Bureau (Plenum), New York, 1984. | MR | Zbl
[34] - Les méthodes nouvelles de la mécanique céleste, Vol. II, Gauthier-Villars, Paris, 1893. | JFM | MR
[35] JR. - "Commuting flows and invariant tori: Korteweg-de Vries", Adv. in Math. 89 (1991), p. 192-216. | MR | Zbl | DOI
[36] - "Characterization of Jacobian varieties in terms of soliton equations", Invent. Math. 83 (1986), p. 333-382. | MR | Zbl | EuDML | DOI
[37] - "On the theory of oscillatory waves", Camb. Trans. 8 (1847), p. 441-473.
[38] - "The continuum limit of theta functions", Comm. Pure Appl. Math. 42 (1989), p. 711-728. | MR | Zbl | DOI
[39] - Linear and Nonlinear Waves. Wiley-Interscience (John Wiley & Sons), New York, 1974. | MR | Zbl
[40] & - "Integrability of nonlinear systems and perturbation theory", in What is Integrability?, Springer Ser. Nonlinear Dynam., Springer, Berlin, 1991, p. 185-250. | MR | Zbl | DOI