Abstract
It is shown in the language of free fermions and the τ functions that the Ablowitz–Ladik (AL) hierarchy and the relativistic Toda lattice hierarchy arise from the A(1)1 reduction of the two-component Toda lattice hierarchy. This result gives us a simple explanation of the reason why the AL hierarchy includes important integrable systems such as the discrete nonlinear Schrodinger equation, the relativistic Toda lattice equation, the Toda field equation, the Davey–Stewartson equation, etc. We also propose a new Backlund transformation (or a discretized time system) for the AL hierarchy.
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