A generalized multi-component Glachette–Johnson (GJ) hierarchy and its integrable coupling system

A new loop algebra is constructed, whose commutation operation defined by us is as simple and straightforward as that in the loop algebra . 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 . A type of multi-component Glachette–Johnson (GJ) hierarchy is obtained. Furthermore, by constructing an expanding loop algebra of the loop algebra , a kind of integrable coupling of the above GJ hierarchy is worked out.