Abstract
We use the Tu‐scheme to construct a general hierarchy of integrable systems associated with a general 2×2 discrete spectral problem. Two new integrable lattice sub‐hierarchies are derived from reductions of the obtained general hierarchy of integrable systems. They are shown to be discrete Hamiltonian systems. The Lax presentations for the two new Hamiltonian sub‐hierarchies are also presented. The Volterra lattice and discrete Burgers equation are rediscovered.
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