Book Review
The AMS does not provide abstracts of book reviews.
You may download the entire review from the links below.
MathSciNet review:
1568140
Full text of review:
PDF
This review is available free of charge.
Book Information:
Author:
Irene Dorfman
Title:
Dirac structures and integrability of nonlinear evolution equations
Additional book information:
Nonlinear Science: Theory and Applications, Wiley \& Sons, New York, 1993, vii+176 pp., US$75.00. ISBN 0-471-93893-9.
E. T. Whittaker, A treatise on the analytical dynamics of particles and rigid bodies, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1988. With an introduction to the problem of three bodies; Reprint of the 1937 edition; With a foreword by William McCrea. MR 992404, DOI 10.1017/CBO9780511608797
Alan Weinstein, Symplectic manifolds and their Lagrangian submanifolds, Advances in Math. 6 (1971), 329–346 (1971). MR 286137, DOI 10.1016/0001-8708(71)90020-X
Robert Brouzet, Systèmes bihamiltoniens et complète intégrabilité en dimension $4$, C. R. Acad. Sci. Paris Sér. I Math. 311 (1990), no. 13, 895–898 (French, with English summary). MR 1084050
Rui L. Fernandes, Completely integrable bi-Hamiltonian systems, J. Dynam. Differential Equations 6 (1994), no. 1, 53–69. MR 1262723, DOI 10.1007/BF02219188
Franco Magri, A simple model of the integrable Hamiltonian equation, J. Math. Phys. 19 (1978), no. 5, 1156–1162. MR 488516, DOI 10.1063/1.523777
V. G. Drinfel′d, Quantum groups, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986) Amer. Math. Soc., Providence, RI, 1987, pp. 798–820. MR 934283
Peter J. Olver, Canonical forms and integrability of bi-Hamiltonian systems, Phys. Lett. A 148 (1990), no. 3-4, 177–187. MR 1068690, DOI 10.1016/0375-9601(90)90775-J
- [1]
- E. T. Whittaker, A treatise on the analytical dynamics of particles and rigid bodies, Cambridge Univ. Press, Cambridge, 1937. MR 992404 (90a:01112)
- [2]
- A. Weinstein, Symplectic manifolds and their Lagrangian submanifolds, Adv. Math. 6 (1971), 329-346. MR 0286137 (44:3351)
- [3]
- R. Brouzet, Systèmes bihamiltoniens et complète intégrabilité en dimension 4, C. R. Acad. Sci. Paris Sér. I Math. 311 (1990), 895-898. MR 1084050 (91j:58071)
- [4]
- R. Fernandes, Completely integrable biHamiltonian systems, J. Dynamics Differential Equations 6 (1994), 53-69. MR 1262723 (95c:58092)
- [5]
- F. Magri, A simple model of the integral Hamiltonian equation, J. Math. Phys. 19 (1978), 1156-1162. MR 488516 (80a:35112)
- [6]
- V. G. Drinfel'd, Quantum groups, Proc. Internat. Congress Math., Berkeley, vol. 1, Amer. Math. Soc., Providence, RI, 1987, pp. 798-820. MR 934283 (89f:17017)
- [7]
- P. J. Olver, Canonical forms and integrability of biHamiltonian systems, Phys. Lett. A 148 (1990), 177-187. MR 1068690 (91j:58066)
Review Information:
Reviewer:
Peter J. Olver
Journal:
Bull. Amer. Math. Soc.
31 (1994), 305-308
DOI:
https://doi.org/10.1090/S0273-0979-1994-00539-7
