Abstract
The Lie-algebraic approach for the dynamic systems associated with a generalization of the Kac-Moody algebras on Riemann surfaces is developed. A technique of solving the inverse scattering problem of operators with spectral parameters on Riemann surfaces is presented. Some equations associated with generalized Kac-Moody algebras are presented. The connection between their hamiltonian structure and deformed Lax representation is discussed as well as its applications to some special perturbations of integrable systems.
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Communicated by Ya. G. Sinai
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Mikhalev, V.G. A generalization of the Kac-Moody algebras with a parameter on an algebraic curve and perturbations of solitons. Commun.Math. Phys. 134, 633–646 (1990). https://doi.org/10.1007/BF02098450
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DOI: https://doi.org/10.1007/BF02098450