The aim of this paper is to construct a six-component integrable hierarchy associated with a matrix spatial spectral problem of arbitrary order. The adopted method is the zero curvature formulation. The corresponding Hamiltonian formulation is furnished by using the trace identity, which guarantees the Liouville integrability for the resulting hierarchy. Two illustrative examples of integrable equations of lower orders are six-component coupled nonlinear Schrödinger equations and modified Korteweg–de Vries equations.

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