Comment on "Space-time shifted solitons and solution interactions for a generalized nonlocal nonlinear Schrödinger equation"
Year: 2026
Type: preprint
Abstract: Zhou and Yu [Appl. Math. Lett. 178 (2026) 109937] studied the space-time shifted nonlocal nonlinear Schrödinger (NLS) equation $iq_t(x,t)=q_{xx}(x,t)-2σq^2(x,t) \bar{q}(x_0-x,t_0+λt),\,\, λ=\pm1$, 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.
Source: arXiv (Cornell University)
Author: Pekcan, Aslı
Institution: Hacettepe University
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212015786