Comment on "Doubly periodic solutions of the focusing nonlinear Schr\"odinger equation: Recurrence, period doubling, and amplification outside the conventional modulation-instability band"

In their interesting article (Physical Review A, Vol. 101, 023843 (2020)) Conforti et al. present doubly periodic (elliptic) solutions of the nonlinear Schr"odinger equation, based on an earlier article by Akhmediev et.al. (Theoretical and Mathematical Physics, Vol. 72, 809 (1987)). We present some notes with respect to correctness, completeness, and representation of the solutions obtained.