Symplectic structures and volume elements in the function space for the cubic schrodinger equation

Duke Mathematical Journal

Volumn 92, Issue 2, 1998, Pages 381-402

  Vaninsky, K L ^a,b  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

^b KANSAS STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039394124     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-98-09211-0     Document Type: Article

References (12)

1. V. I. Arnold, Mathematical Methods of Classical Mechanics, Grad. Texts, in Math. 60, Springer-Verlag, New York, 1978.
2. R. Donagi and E. Witten, Supersymmetric Yang-Mills theory and integrable systems, Nuclear Phys. B 460 (1996), 299-334.
3. A. R. Its, Inversion of hyperelliptic integrals, and integration of nonlinear differential equations, Vestnik Leningrad. Univ. 1976, 39-46.
4. I. M. Krichever, Integration of nonlinear equations by the methods of the algebraic geometry, Funktsional. Anal, i Prolizhen 11 (1977), 15-31.
5. I. M. Krichever, The averaging method for two-dimensional integrable equations, Functional Anal. Appl. 22 (1988), 200-213.
6. I. M. Krichever and D. H. Phong, On the integrable geometry of soliton equations and N = 2 supersymmetric gauge theories, J. Differential Geom. 45 (1997), 349-389.
7. H. P. McKean, “T race formulas and the canonical 1-form” in Algebraic Aspects of Integrable systems. In memory of Irene Dorfman, ed. A. S. Fokas and I. M. Gelfand, Progr. Nonlinear Differential Equations Appl. 26, Birkhäuser, Boston, 1997, 217-235.
8. H. P. McKean and K. L. Vaninsky, Action-angle variables for cubic Schrödinger equation, Comm. Pure Appl. Math. 50 (1997), 489-562.
9. H. P. McKean and K. L. Vaninsky, Cubic Schrödinger: The petit canonical ensemble in action-angle variables, Comm. Pure Appl. Math. 50 (1997), 593-622.
10. N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation, and confinement in N = 2 supersymmetric Yang-Mills theory, Nuclear Phys. B 426 (1994), 1952.
11. L. Vaninsky, “Invariant Gibbsian Measures of the Klein-Gordon equation” in Stochastic Analysis, (Ithaca, N.Y., 1993), ed. M. C. Cranston and M. A. Pinsky, Proc. Sympos. Math. 57, Amer. Math. Soc., Providence, 1995,495-510.
12. L. Vaninsky, “Gibbs’ states for Moser-Calogero potentials” in Proceedings of the Conference on Exactly Soluble Models in Statistical Mechanics: Historical Perspectives and Current Status (Boston, 1996), Internat. J. Modern Phys. B 11, World Sci., Singapore, 1997, 203-211.