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Quasigraded Lie algebras and modified Toda field equations. (English) Zbl 1128.37046
In the present study the author constructs a family of quasigraded Lie algebras that coincide with the deformation of the “principal” subalgebras of the loop algebras. The author defines a new type of the quasigraded Lie algebras admitting Konstant-Adler-Symes scheme. For this purpose the author explicitly constructs dual space, coadjoint action, its invariants and Lie-Poisson brackets for the case of Lie algebra. As a result the author obtains new integrable hierarchies satisfying zero-curvature conditions associated with corresponding Lie algebras.

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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