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A Lie algebra containing four parameters for the generalized Dirac hierarchy. (English) Zbl 1218.37087

Summary: A Lie algebra containing four parameters is obtained, whose commutation operation is concise, and the corresponding computing formula of constant \(\gamma \) in the variational identity is presented in this paper. As application, a new Liouville integrable hierarchy which can be reduced to the Dirac hierarchy is derived by designing a special isospectral problem. We call it generalized Dirac hierarchy.

MSC:

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37K30 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures
17B80 Applications of Lie algebras and superalgebras to integrable systems
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References:

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