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Two hierarchies of multi-component Kaup–Newell equations are derived from an arbitrary order matrix spectral problem, including positive non-isospectral Kaup–Newell hierarchy and negative non-isospectral Kaup–Newell hierarchy. Moreover, new integrable couplings of the resulting Kaup–Newell soliton hierarchies are constructed by enlarging the associated matrix spectral problem.
A new isospectral problem is designed and the multi-component second mKdV equation is worked out from it. It follows that two distinct types of integrable couplings of the multi-component second mKdV equation are obtained by constructing two types of new loop algebras. As its reduction, two distinct types of integrable couplings of the multi-component KdV equation, the multi-component mKdV equation...
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