Comment on "Space-time shifted solitons and solution interactions for a generalized nonlocal nonlinear Schrödinger equation"
Abstract
Zhou and Yu [Appl. Math. Lett. 178 (2026) 109937] studied the space-time shifted nonlocal nonlinear Schrödinger (NLS) equation iqt(x,t)=qxx(x,t)−2σq2(x,t) q̅(x0−x,t0+λt), λ=±1, and claimed that for both choices of λ the equation is integrable. Here we examine this claim from the perspective of reductions of the standard integrable NLS system. We find that the compatibility of the equation with the NLS system is true only when there is no time reversal in the argument. In other words, for this equation it requires λ=1 and t0=0. The case with λ=−1 is a valid nonlocal equation, but cannot be derived from the standard NLS system by the corresponding complex conjugate shifted nonlocal reduction, and its integrability therefore does not follow from that integrable NLS system. We also discuss the equivalence between shifted (with real shifts) and unshifted nonlocal reductions and give the adjusted form of the Hirota bilinear equation.
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BibTeX
@misc{pekcan2026comment,
title = {{Comment on "Space-time shifted solitons and solution interactions for a generalized nonlocal nonlinear Schrödinger equation"}},
author = {Aslı Pekcan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05483},
eprint = {2609.05483},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05483},
}
RIS
TY - UNPB
TI - Comment on "Space-time shifted solitons and solution interactions for a generalized nonlocal nonlinear Schrödinger equation"
AU - Aslı Pekcan
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.05483
UR - https://arxiv.org/abs/2609.05483
AB - Zhou and Yu [Appl. Math. Lett. 178 (2026) 109937] studied the space-time shifted nonlocal nonlinear Schrödinger (NLS) equation iq_t(x,t)=q_xx(x,t)−2σq^2(x,t) q̅(x_0−x,t_0+λt), λ=±1, and claimed that for both choices of λ the equation is integrable. Here we examine this claim from the perspective of reductions of the standard integrable NLS system. We find that the compatibility of the equation with the NLS system is true only when there is no time reversal in the argument. In other words, for this equation it requires λ=1 and t_0=0. The case with λ=−1 is a valid nonlocal equation, but cannot be derived from the standard NLS system by the corresponding complex conjugate shifted nonlocal reduction, and its integrability therefore does not follow from that integrable NLS system. We also discuss the equivalence between shifted (with real shifts) and unshifted nonlocal reductions and give the adjusted form of the Hirota bilinear equation.
ER -