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A generalized multi-component Glachette-Johnson (GJ) hierarchy and its integrable coupling system. (English) Zbl 1048.37063
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 systems, integrability tests, bi-Hamiltonian structures, hierarchies 17B80 Applications of Lie algebras to integrable systems 37K30 Relations of infinite-dimensional systems with algebraic structures
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