  In the recent paper (R. Willox and M. Hattori, arXiv:1406.5828), an
integrable discretization of the nonlinear Schr\"odinger (NLS) equation is
studied, which, they think, was discovered by Date, Jimbo and Miwa in 1983 and
has been completely forgotten over the years. In fact, this discrete NLS
hierarchy can be directly obtained from an elementary auto-B\"acklund
transformation for the continuous NLS hierarchy and has been known since 1982.
Nevertheless, it has been rediscovered again and again in the literature
without attribution, so we consider it meaningful to mention overlooked
original references on this discrete NLS hierarchy.
