Comment on "Discretisations of constrained KP hierarchies"

TL;DR

This paper comments on a recent discretization of the nonlinear Schrödinger equation, clarifying its historical origins and emphasizing overlooked prior work that predates the recent rediscovery.

Contribution

It highlights the historical background of a discrete NLS hierarchy, correcting the attribution and emphasizing its prior discovery in 1982.

Findings

The discrete NLS hierarchy can be derived from an auto-Bäcklund transformation.

The hierarchy was originally discovered in 1982 and has been rediscovered without proper attribution.

The recent paper's claimed discovery was actually known since 1982.

Abstract

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.