Abstract
We study the Lie geometric structure behind the Hamiltonian structure of the Korteweg deVries type equations.
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References
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.
P.D. Lax, Integrals of Nonlinear Equations of Evolution and Solitary Waves, Comm. Pure Appl. Math., Vol. 21, 1968, 467–490.
J. Marsden, Applications of Global Analysis in Mathematical Physics, Chapter 6, Publish or Perish, Inc., 1974.
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).
B. Kostant, to appear.
B. Symes, to appear.
O.I. Boboyovlensky, On Perturbations of the Periodic Toda Lattices, Comm. Math. Physics, 51, 1976, 201–209.
L. Dikii, Hamiltonian Systems Connected with the Rotation Group, Funkcional'nyi Analiz i ego Prilozenija, Vol. 6, No. 4, 83–84.
J. Moser, Three Integrable Hamiltonian Systems Connected with Isospectral Deformations, Adv. in Math., Vol. 16, No. 2, May 1975.
D. Kazhdan, B. Kostant, and S. Sternberg, Hamiltonian Group Actions and Dynamical Systems of Calogero Type, C.P.A.M., Vol. 23, 1–27, (1978).
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.
S.V. Manakov, Note on the Integration of Euler's Equations of the Dynamics of an n-Dimensional Rigid Body, Funkcional'nyi Analiz i ego Prilozenija, Vol. 10, No. 4, 93–94, October–December (1976).
I.M. Gel'fand and L.A. Dikii, The Resolvant and Hamiltonian Systems, Funkcional'nyi Analiz i ego Prilozenija, Vol. 11, No. 2, 11–27, April–June, 1977.
P. Lax, Almost Periodic Solutions of the KdV Equations, SIAMS Reviews, 1976.
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).
B.A. Kupershmidt and Yu I. Manin, Equations of Long Waves with a Free Surface. II. Hamiltonian Structure and Higher Equations, Funkcional'nyi Analiz i ego Prilozenija, Vol. 12, No. 1, 25–37, January–March (1978).
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Adler, M. (1979). On a trace functional for formal pseudo-differential operators and the Hamiltonian structure of korteweg-devries types equations. In: Grmela, M., Marsden, J.E. (eds) Global Analysis. Lecture Notes in Mathematics, vol 755. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069801
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DOI: https://doi.org/10.1007/BFb0069801
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