Comment on "Rogue waves on the double-periodic background in the focusing nonlinear Schr\"odinger equation"
Hans Werner Schuermann, Valery Serov
TL;DR
This paper critically examines a previous claim about rogue wave solutions in the nonlinear Schrödinger equation, demonstrating that the proposed solutions do not actually satisfy the equation, thus refuting the original claim.
Contribution
It provides a rigorous critique showing that the solutions claimed in prior work are invalid, clarifying the mathematical inaccuracies in the original claim.
Findings
The solutions do not satisfy the nonlinear Schrödinger equation.
The original claim of rogue wave solutions is incorrect.
The critique clarifies the mathematical errors in the previous work.
Abstract
Some years ago, Chen, Pelinovsky, and White claimed existence of certain solutions of the nonlinear Schr\"odinger equation for modelling rogue waves [arXiv: 1909.08165v1 (2019)]. It is the aim of this Comment to outline that this claim is faulty. -- The solutions presented do not satisfy the nonlinear Schr\"odinger equation.
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Taxonomy
TopicsNonlinear Waves and Solitons · Nonlinear Photonic Systems · Quantum Mechanics and Non-Hermitian Physics