Abstract
We consider a dynamic system on the extended phase space to the initial Lie algebra and study its generalized Hamiltonian and integrability in the cases when the initial Lie algebra coincides with the Grassmann algebra of pseudodifferential operators on the real line and on the centrally extended affine Lie algebra.
Similar content being viewed by others
Literature cited
R. Abraham and J. Marsden,Foundations of Mechanics, Benjamin, London (1978).
L. Faddeev and L. Takhtadjan,The Hamiltonian Approach to Soliton Theory, Springer, New York (1986).
P. Olver,Applications of Lie Groups to Differential Equations, Springer, New York (1986).
W. Oevel and W. Strampp, “Constrained RP-hierarchy and bi-Hamiltonian structures,”Comm. Math. Physics,157 (1), 51–81 (1993).
A. Prykarpatsky, R. Samuliak, D. Blackmore, W. Stramp, and Yu. Sydorenko, “Some remarks on Lagrangian and Hamiltonian formalism, related to infinite-dimensional dynamical systems with symmetries,”Condensed Matter Physics, No. 6 (1995).
Additional information
Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 106–115.
Rights and permissions
About this article
Cite this article
Prikarpats'kii, Y.A. The structure of integrable Lax flows on nonlocal manifolds: Dynamic systems with sources. J Math Sci 96, 3030–3037 (1999). https://doi.org/10.1007/BF02169701
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02169701