Notes on “A integrable lattice hierarchy based on Suris system: N-fold Darboux transformation and conservation laws” [Nonlinear. Dyn. (2018) 91:625–639

Abstract

We point out that the Hamiltonian structure of the integrable lattice hierarchy in “A integrable lattice hierarchy based on Suris system: N-fold Darboux transformation and conservation laws” [Nonlinear. Dyn. (2018) 91:625–639] is not correct. Then, we establish a correct Hamiltonian structure by the trace identity. Further, we also prove that the integrable lattice hierarchy has bi-Hamiltonian structure. Thus, the Liouville integrability of the integrable lattice hierarchy is obtained.