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

TL;DR

This paper critically examines the doubly periodic solutions of the nonlinear Schr"odinger equation presented by Conforti et al., discussing their correctness, completeness, and how they are represented.

Contribution

It provides a detailed critique and clarification of the solutions proposed by Conforti et al., highlighting issues and offering insights into their mathematical structure.

Findings

Identifies potential inaccuracies in the original solutions

Clarifies the mathematical representation of solutions

Highlights the importance of correctness and completeness in solution derivation

Abstract

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.