On a trace functional for formal pseudo-differential operators and the Hamiltonian structure of korteweg-devries types equations
Part of the Lecture Notes in Mathematics book series (LNM, volume 755)
- 301 Downloads
We study the Lie geometric structure behind the Hamiltonian structure of the Korteweg deVries type equations.
KeywordsPoisson Bracket Invariant Manifold Poisson Structure Hamiltonian Structure Hamiltonian Vector Field
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Unable to display preview. Download preview PDF.
- 1.I.M. Gel'fand and L.A. Dikii, Fractional Powers of Operators and Hamiltonian Systems, Funkcional'nyi i ego Prilozenija, Vol. 10, No. 4, 1976.Google Scholar
- 3.J. Marsden, Applications of Global Analysis in Mathematical Physics, Chapter 6, Publish or Perish, Inc., 1974.Google Scholar
- 4.M. Adler, On a Trace Functional for Formal Pseudo-Differential Operators and the Symplectic Structure of the Korteweg-deVries Type Equations, to appear in Inventiones, (also obtainable in slightly different from as an MRC Tech. Report, University of Wisconsin at Madison, 1978).Google Scholar
- 5.B. Kostant, to appear.Google Scholar
- 6.B. Symes, to appear.Google Scholar
- 8.L. Dikii, Hamiltonian Systems Connected with the Rotation Group, Funkcional'nyi Analiz i ego Prilozenija, Vol. 6, No. 4, 83–84.Google Scholar
- 9.J. Moser, Three Integrable Hamiltonian Systems Connected with Isospectral Deformations, Adv. in Math., Vol. 16, No. 2, May 1975.Google Scholar
- 11.M. Adler, Completely Integrable Systems and Symplectic Actions, MRC Tech. Report #1830, University of Wisconsin-Madison, 1978, an augmented version to appear in J.M.P., 1979.Google Scholar
- 14.P. Lax, Almost Periodic Solutions of the KdV Equations, SIAMS Reviews, 1976.Google Scholar
- 15.I.M. Gel'fand, Yu I. Manin, and M.A. Shubin, Poisson Brackets and the Kernel of a Variational Derivative in the Formal Variational Calculus, Funkcional'nyi Analiz i ego Prilozenija, Vol. 10, No. 4, (1976).Google Scholar
© Springer-Verlag 1979