Abstract
A new loop algebra 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 G M . A type of multi-component Glachette–Johnson (GJ) hierarchy is obtained. Furthermore, by constructing an expanding loop algebra F M of the loop algebra G M , a kind of integrable coupling of the above GJ hierarchy is worked out.
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