Dirac structures of integrable evolution equations
Authors
Abstract
An algebraic theory of Dirac structures is presented, enclosing finite-dimensional pre-symplectic and Poisson structures, as well as their infinite-dimensional analogs determined by local operators. The generalized Lenard scheme of integrability is considered together with examples of its action.
Citation
- Journal: Physics Letters A
- Year: 1987
- Volume: 125
- Issue: 5
- Pages: 240–246
- Publisher: Elsevier BV
- DOI: 10.1016/0375-9601(87)90201-5
BibTeX
@article{Dorfman_1987,
title={{Dirac structures of integrable evolution equations}},
volume={125},
ISSN={0375-9601},
DOI={10.1016/0375-9601(87)90201-5},
number={5},
journal={Physics Letters A},
publisher={Elsevier BV},
author={Dorfman, Irene Ya.},
year={1987},
pages={240--246}
}
References
- Zacharov, Funkt. Anal. Appl. (1971)
- Gardner, C. S. Korteweg-de Vries Equation and Generalizations. IV. The Korteweg-de Vries Equation as a Hamiltonian System. Journal of Mathematical Physics vol. 12 1548–1551 (1971) – 10.1063/1.1665772
- Gelfand, Funkt. Anal. Appl. (1979)
- Frolov, N. N. Self-adjointness of elliptic operators with infinitely many variables. Functional Analysis and Its Applications vol. 14 71–72 (1980) – 10.1007/bf01078432
- Gelfand, Funkt. Anal. Appl. (1981)
- Krichever, Usp. Mat. Nauk (1980)
- Courant, (1986)
- Magri, F. A simple model of the integrable Hamiltonian equation. Journal of Mathematical Physics vol. 19 1156–1162 (1978) – 10.1063/1.523777
- Gelfand, Usp. Mat. Nauk (1975)
- Kirillov, Usp. Mat. Nauk. (1976)
- Dubrovin, Dokl. Akad. Nauk SSSR (1983)
- Faddeev, L. D. The Feynman integral for singular Lagrangians. Theoretical and Mathematical Physics vol. 1 1–13 (1969) – 10.1007/bf01028566
- Dorfman, (1984)
- Fuchssteiner, B. Application of hereditary symmetries to nonlinear evolution equations. Nonlinear Analysis: Theory, Methods & Applications vol. 3 849–862 (1979) – 10.1016/0362-546x(79)90052-x
- Gelfand, (1978)
- Sokolov, Dokl. Akad. Nauk SSSR (1984)
- Fokas, A. S. & Fuchssteiner, B. The hierarchy of the Benjamin-Ono equation. Physics Letters A vol. 86 341–345 (1981) – 10.1016/0375-9601(81)90551-x
- Oevel, W. & Fuchssteiner, B. Explicit formulas for symmetries and conservation laws of the Kadomtsev-Petviashvili equation. Physics Letters A vol. 88 323–327 (1982) – 10.1016/0375-9601(82)90605-3
- Dorfman, (1986)
- Fokas, (1986)