A reply to a comment: a note on an integrable discretization of the nonlinear Schrödinger equation

The splitting approach of the previous paper by Suris (Suris Yu B 1997 Inverse Problems 13 1121-36) is applied to the original Ablowitz-Ladik discretization of nonlinear Schrodinger equations (NLS). The outcome is the realization of the latter free of nonlocalities. The severe grid-size restriction pointed out in the comment by Black et al (Black W, Weidemann J A C and Herbst B M 1999 Inverse Problems 15 807-10) does not appear in this construction.