Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Full text of review: PDF
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.

References [Enhancements On Off] (What's this?)

  • [1] 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
  • [2] Alan Weinstein, Symplectic manifolds and their Lagrangian submanifolds, Advances in Math. 6 (1971), 329–346 (1971). MR 0286137
  • [3] 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
  • [4] Rui L. Fernandes, Completely integrable bi-Hamiltonian systems, J. Dynam. Differential Equations 6 (1994), no. 1, 53–69. MR 1262723, 10.1007/BF02219188
  • [5] Franco Magri, A simple model of the integrable Hamiltonian equation, J. Math. Phys. 19 (1978), no. 5, 1156–1162. MR 488516, 10.1063/1.523777
  • [6] 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
  • [7] Peter J. Olver, Canonical forms and integrability of bi-Hamiltonian systems, Phys. Lett. A 148 (1990), no. 3-4, 177–187. MR 1068690, 10.1016/0375-9601(90)90775-J

Review Information:

Reviewer: Peter J. Olver
Journal: Bull. Amer. Math. Soc. 31 (1994), 305-308