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On the symplectic structure of the phase space for periodic $KdV$, Toda, and defocusing NLS

D. Bättig, A. M. Bloch, J.-C. Guillot, and T. Kappeler
Source: Duke Math. J. Volume 79, Number 3 (1995), 549-604.
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Primary Subjects: 58F07
Secondary Subjects: 34A55, 34L05, 35Q53
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077285350
Mathematical Reviews number (MathSciNet): MR1355177
Zentralblatt MATH identifier: 0855.58035
Digital Object Identifier: doi:10.1215/S0012-7094-95-07914-9

References

[AN] Arnold, V. I. and Novikov, S. P. and Wassermann, G., eds., Dynamical Systems IV, Encyclopaedia of Mathematical Sciences, vol. 4, Springer-Verlag, Berlin, 1990.
Mathematical Reviews (MathSciNet): MR90j:58039
Zentralblatt MATH: 0778.00008
[At] M. Atiyah, Convexity and commuting Hamiltonians, Bull. London Math. Soc. 14 (1982), no. 1, 1–15.
Mathematical Reviews (MathSciNet): MR83e:53037
Zentralblatt MATH: 0482.58013
Digital Object Identifier: doi:10.1112/blms/14.1.1
[BBGK] D. Bättig, A. Bloch, J. C. Guillot, and T. Kappeler, La structure symplectique de l'espace de phase de l'équation Korteweg-de Vries périodique, C. R. Acad. Sci. Paris Sér. I Math. 317 (1993), no. 11, 1019–1022.
Mathematical Reviews (MathSciNet): MR94i:58062
Zentralblatt MATH: 0816.35119
[BGGK1] D. Bättig, B. Grébert, J.-C. Guillot, and T. Kappeler, Foliation of phase space for the cubic nonlinear Schrödinger equation, Compositio Math. 85 (1993), no. 2, 163–199.
Mathematical Reviews (MathSciNet): MR94c:58155
Zentralblatt MATH: 0783.35068
[BGGK2] D. Bättig, B. Grébert, J.-C. Guillot, and T. Kappeler, Fibration of the phase space of the periodic Toda lattice, J. Math. Pures Appl. (9) 72 (1993), no. 6, 553–565.
Mathematical Reviews (MathSciNet): MR95b:58073
Zentralblatt MATH: 0863.58032
[BKM1] D. Bättig, T. Kappeler, and B. Mityagin, On the Korteweg-de Vries equation: Frequencies and initial value problem, preprint.
Mathematical Reviews (MathSciNet): MR1491035
Zentralblatt MATH: 0899.35096
Digital Object Identifier: doi:10.2140/pjm.1997.181.1
[BKM2] D. Bättig, T. Kappeler, and B. Mityagin, On the Korteweg-de Vries equation: Convergent Birkhoff normal form, Inst. Haute Etudes Sci. preprint.
Mathematical Reviews (MathSciNet): MR1409041
Zentralblatt MATH: 0868.35099
Digital Object Identifier: doi:10.1006/jfan.1996.0111
[Bo] J. Bourgain, Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II. The KdV-equation, Geom. Funct. Anal. 3 (1993), no. 3, 209–262.
Mathematical Reviews (MathSciNet): MR95d:35160b
Zentralblatt MATH: 0787.35098
Digital Object Identifier: doi:10.1007/BF01895688
[DLT] P. Deift, F. Lund, and E. Trubowitz, Nonlinear wave equations and constrained harmonic motion, Comm. Math. Phys. 74 (1980), no. 2, 141–188.
Mathematical Reviews (MathSciNet): MR82g:35102
Zentralblatt MATH: 0435.35072
Digital Object Identifier: doi:10.1007/BF01197756
Project Euclid: euclid.cmp/1103907980
[Du] J. J. Duistermaat, On global action-angle coordinates, Comm. Pure Appl. Math. 33 (1980), no. 6, 687–706.
Mathematical Reviews (MathSciNet): MR82d:58029
Zentralblatt MATH: 0439.58014
Digital Object Identifier: doi:10.1002/cpa.3160330602
[FIT] A. Finkel, E. Isaacson, and E. Trubowitz, An explicit solution of the inverse periodic problem for Hill's equation, SIAM J. Math. Anal. 18 (1987), no. 1, 46–53.
Mathematical Reviews (MathSciNet): MR88d:34037
Zentralblatt MATH: 0622.34021
Digital Object Identifier: doi:10.1137/0518003
[FM] H. Flaschka and D. W. McLaughlin, Canonically conjugate variables for the Korteweg-de Vries equation and the Toda lattice with periodic boundary conditions, Progr. Theoret. Phys. 55 (1976), no. 2, 438–456.
Mathematical Reviews (MathSciNet): MR53:7179
Zentralblatt MATH: 01662199
Digital Object Identifier: doi:10.1143/PTP.55.438
[Fo] A. T. Fomenko, The topology of surfaces of constant energy in integrable Hamiltonian systems and obstructions to integrability, Math. USSR-Izv. 29 (1987), 629–658.
Zentralblatt MATH: 0649.58019
[Fr] J. P. Françoise, Calculs explicites d'action-angles, Systemes Dynamiques Non Lineaires: Integrabilite et Comportement Qualitatif ed. P. Winternitz, Sém. Math. Sup., vol. 102, Presses de l'Universite de Montreal, Montreal, 1986, pp. 101–120.
Mathematical Reviews (MathSciNet): MR88g:58079
Zentralblatt MATH: 0642.58027
[Ga] J. B. Garnett, Applications of Harmonic Measures, University of Arkansas Lecture Notes in Math., vol. 8, Wiley, New York, 1986.
Mathematical Reviews (MathSciNet): MR88j:30054
Zentralblatt MATH: 0623.31001
[GK] I. C. Gohberg and M. G. Krein, Introduction to the theory of linear nonselfadjoint operators, Translated from the Russian by A. Feinstein. Translations of Mathematical Monographs, Vol. 18, American Mathematical Society, Providence, R.I., 1969.
Mathematical Reviews (MathSciNet): MR39:7447
Zentralblatt MATH: 0181.13504
[GS] V. Guillemin and S. Sternberg, Convexity properties of the moment mapping, Invent. Math. 67 (1982), no. 3, 491–513.
Mathematical Reviews (MathSciNet): MR83m:58037
Zentralblatt MATH: 0503.58017
Digital Object Identifier: doi:10.1007/BF01398933
[GT1] J. B. Garnett and E. Trubowitz, Gaps and bands of one-dimensional periodic Schrödinger operators, Comm. Math. Helv. 59 (1984), no. 2, 258–312.
Mathematical Reviews (MathSciNet): MR85i:34004
Zentralblatt MATH: 0554.34013
Digital Object Identifier: doi:10.1007/BF02566350
[GT2] J. B. Garnett and E. Trubowitz, Gaps and bands of one-dimensional periodic Schrödinger operators II, Comm. Math. Helv. 62 (1987), no. 1, 18–37.
Mathematical Reviews (MathSciNet): MR88g:34028
Zentralblatt MATH: 0649.34034
Digital Object Identifier: doi:10.1007/BF02564436
[Ka] T. Kappeler, Fibration of the phase space for the Korteweg-de Vries equation, Ann. Inst. Fourier (Grenoble) 41 (1991), no. 3, 539–575.
Mathematical Reviews (MathSciNet): MR92k:58212
Zentralblatt MATH: 0731.58033
[Kn] H. Knörrer, Geodesics on quadrics and a mechanical problem of C. Neumann, J. Reine Angew. Math. 334 (1982), 69–78.
Mathematical Reviews (MathSciNet): MR84b:58089
Zentralblatt MATH: 0478.58014
[Ma] F. Magri, A simple model of the integrable Hamiltonian equation, J. Math. Phys. 19 (1978), no. 5, 1156–1162.
Mathematical Reviews (MathSciNet): MR80a:35112
Zentralblatt MATH: 0383.35065
Digital Object Identifier: doi:10.1063/1.523777
[Mo] J. Moser, Various aspects of integrable Hamiltonian systems, Dynamical Systems (C.I.M.E. Summer School, Bressanone, 1978), Progr. Math., vol. 8, Birkhauser, Boston, 1980, pp. 233–289.
Mathematical Reviews (MathSciNet): MR83a:58042a
Zentralblatt MATH: 0468.58011
[Moe] P. van Moerbeke, The spectrum of Jacobi matrices, Invent. Math. 37 (1976), no. 1, 45–81.
Mathematical Reviews (MathSciNet): MR58:31226
Zentralblatt MATH: 0361.15010
Digital Object Identifier: doi:10.1007/BF01418827
[MT] H. McKean and E. Trubowitz, Hill's operator and hyperelliptic function theory in the presence of infinitely many branch points, Comm. Pure Appl. Math. 29 (1976), no. 2, 143–226.
Mathematical Reviews (MathSciNet): MR55:761
Zentralblatt MATH: 0339.34024
Digital Object Identifier: doi:10.1002/cpa.3160290203
[NV1] S. P. Novikov and A. P. Veselov, On Poisson brackets compatible with algebraic geometry and Korteweg-de Vries dynamics on the set of finite zone potentials, Soviet Math. Dokl. 26 (1982), 357–263.
Zentralblatt MATH: 0555.35106
[NV2] A. P. Veselov and S. P. Novikov, Poisson brackets and complex tori, Trudy Mat. Inst. Steklov. 165 (1984), 49–61.
Mathematical Reviews (MathSciNet): MR86c:58076
Zentralblatt MATH: 0565.58022
[PT] J. Pöschel and E. Trubowitz, Inverse Spectral Theory, Pure and Applied Mathematics, vol. 130, Academic Press, New York, 1987.
Mathematical Reviews (MathSciNet): MR89b:34061
Zentralblatt MATH: 0623.34001
[V] A. P. Veselov, Finite zone potentials and integrable systems on the sphere with quadratic potential, Functional Anal. Appl. 14 (1980), 37–39.
Zentralblatt MATH: 0574.34001
Mathematical Reviews (MathSciNet): MR565097
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