Superregular solitonic solutions of the defocusing nonlocal nonlinear Schrodinger equation and their novel perspectives
Abstract
Previous studies have indicated that the local defocusing nonlinear Schrödinger equation (NLSE) is modulationally stable. Therefore, superregular solitonic solutions characterizing the nonlinear evolution of modulational instability under weak localized perturbations do not exist. In this work, we study the nonlinear stage of the modulation instability of a condensate in the framework of the defocusing nonlocal NLSE. By using the dressing method and Joukowski transformation, we systematically derive the general N-solitonic solution of the defocusing nonlocal NLSE, and the explicit expressions for one-solitonic, two-solitonic and superregular two-solitonic solutions are provided. Then dynamics of these solutions is also examined. We find that these solutions show a much wider variety than those in the local NLSE, such as the one solitonic solution composed of two interacting wave components and the two-solitonic solution containing four wave components. Finally, the accuracy and noise robustness of the analytical solutions are confirmed by numerical simulations. Such results advance the theory of superregular solitonic solutions in nonlocal systems and offer new physical understanding of wave propagation in nonlocal nonlinear media.
Related
- Existence of solutions for a large defocusing parameter in a strongly indefinite Schrödinger equation
- Global well-posedness and scattering for the defocusing nonlinear Schrödinger equation below energy space
- Global well-posedness and scattering for the three-dimensional defocusing cubic Schrödinger equation in Hs, s>1/2
- Blow-up for energy supercritical defocusing nonlinear Schrödinger equations in dimensions three, four and five
- Global well-posedness and scattering of energy-critical defocusing nonlinear Schrödinger equation on high-dimensional hyperbolic spaces
BibTeX
@misc{xia2026superregular,
title = {{Superregular solitonic solutions of the defocusing nonlocal nonlinear Schrodinger equation and their novel perspectives}},
author = {Duan-Yun Xia and Xiu-Bin Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33560},
eprint = {2610.33560},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33560},
}
RIS
TY - UNPB
TI - Superregular solitonic solutions of the defocusing nonlocal nonlinear Schrodinger equation and their novel perspectives
AU - Duan-Yun Xia
AU - Xiu-Bin Wang
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33560
UR - https://arxiv.org/abs/2610.33560
AB - Previous studies have indicated that the local defocusing nonlinear Schrödinger equation (NLSE) is modulationally stable. Therefore, superregular solitonic solutions characterizing the nonlinear evolution of modulational instability under weak localized perturbations do not exist. In this work, we study the nonlinear stage of the modulation instability of a condensate in the framework of the defocusing nonlocal NLSE. By using the dressing method and Joukowski transformation, we systematically derive the general N-solitonic solution of the defocusing nonlocal NLSE, and the explicit expressions for one-solitonic, two-solitonic and superregular two-solitonic solutions are provided. Then dynamics of these solutions is also examined. We find that these solutions show a much wider variety than those in the local NLSE, such as the one solitonic solution composed of two interacting wave components and the two-solitonic solution containing four wave components. Finally, the accuracy and noise robustness of the analytical solutions are confirmed by numerical simulations. Such results advance the theory of superregular solitonic solutions in nonlocal systems and offer new physical understanding of wave propagation in nonlocal nonlinear media.
ER -