Integrable Evolutionary Equations Via Lie Algebras on Hyperelliptic Curves
We construct a family of quasi-graded algebras on hyperelliptic curves that admit the Kost ant-Adler scheme. We use them to find new integrable nonlinear evolutionary equations which admit zero-curvature representations.
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- 1.Tahtadjan, L. and Faddejev, L. (1987) Hamiltonian approach in the theory of solitons. Springer, Berlin.Google Scholar
- 3.Reyman A.G. and Semenov Tian-Shansky M. A. (1980) Current algebras and nonlinear equations in partial derivatives, Doklady of the Academy of sciences of USSR, 251, No 6, 1310–1324.Google Scholar
- 4.Sklyanin E.K. (1979) On complete integrability of the Landau-Lifschits equations, preprint LOMIE-3-79.Google Scholar
- 5.Holod P.I. (1984) Hamiltonian Systems connected with the anisotropic affine Lie algebras and higher Landau-Lifschits equations, Doklady of the Academy of sciences of Ukrainian SSR, 276, No 5., 5–8.Google Scholar
- 6.Holod P.I. (1984) Finite-gap extension of the hamiltonian equations for Kirchhoff’ s problem in Steklov’s integrable case, preprint ITF-84-87R.Google Scholar
- 7.Holod P.I. (1987) Two-dimensional generalization of the integrable equation of Steklov of the motion of the rigid body in the liquid, Doklady of the Academy of sciences of the USSR, 292, No 5, 1087–1091.Google Scholar
- 8.Sidorenko Yu. N. (1987) The elliptic bundle and generating operators, Zapiski Nauch. Sem. LOMI, 161. Google Scholar
- 9.Holod P.I. and Skrypnyk T.V. (2000) Anisotropic Quasigraduated Lie Algebras on Hyperelliptic Curves and Integrable Hammiltonian Systems, Naukovi Zapysky NaUKMA 8, (Phys-Math Science), 20–25.Google Scholar
- 10.Skrypnyk T.V. (2000) Lie algebras on hyperelliptic curves and finite-dimensional integrable systems, Proceedings of the XXIII International Colloquium on the group theoretical methods in Physics, Dubna, Russia, nlin.SI-0010005.Google Scholar