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How to construct a variable coefficient integrable coupling equation hierarchy is an important problem. In this paper, we present new Lax pairs with some arbitrary functions and generate a variable coefficient integrable coupling of Ablowitz-Kaup-Newell-Segur hierarchy from a zero-curvature equation. Then the Hamiltonian structure of the variable coefficient coupling equation hierarchy is derived from the variational trace identity. It is also indicated that this method is an efficient and straightforward way to construct the variable coefficient integrable coupling equation hierarchy.

Constructing a Variable Coefficient Integrable Coupling Equation Hierarchy and its Hamiltonian Structure