A generalized multi-component Glachette-Johnson (GJ) hierarchy and its integrable coupling system. (English) Zbl 1048.37063

Zhang, Yufeng

Chaos Solitons Fractals 21, No. 2, 305-310 (2004).

Summary: A new loop algebra \(\widetilde G_M\) is constructed, whose commutation operation defined by us is as simple and straightforward as that in the loop algebra \(A_1\). It follows that a general scheme for generating multi-component integrable hierarchies is proposed. As an illustrative example, a new isospectral problem is established by taking advantage of \(\widetilde G_M\). A type of multi-component Glachette–Johnson (GJ) hierarchy is obtained. Furthermore, by constructing an expanding loop algebra \(\widetilde F_M\) of the loop algebra \(\widetilde G_M\), a kind of integrable coupling of the above GJ hierarchy is worked out.

MSC:

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

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