Rogue wave patterns associated with Adler–Moser polynomials in the nonlocal nonlinear Schrödinger equation

Authors

Tingyou Wang
Zhenyun Qin
Gui Mu
Fuzhuang Zheng
Zhijun Qiao, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

10-3-2025

Abstract

In this paper, novel rogue wave patterns in the nonlocal nonlinear Schrödinger equation (NLS) are investigated by means of asymptotic analysis, including heart-pentagon, oval-triangle, and fan-triangle. It is demonstrated that when multiple free parameters get considerably large, rogue wave patterns can approximately be predicted by the root structures of Adler–Moser polynomials. These polynomials, which extend the Yablonskii–Vorob’ev polynomial hierarchy, exhibit richer geometric shapes in their root distributions. The (x,t)-plane is partitioned into three regions and through a combination of asymptotic results in different regions, unreported rogue wave patterns can be probed. Predicted solutions are compared with true rogue waves in light of graphical illustrations and numerical confirmation, which reveal excellent agreement between them.

Comments

Original published version available at https://doi.org/10.1016/j.chaos.2025.116856

Recommended Citation

Yang, Bo, and Jianke Yang. "Rogue wave patterns associated with Adler–Moser polynomials in the nonlinear Schrödinger equation." Applied Mathematics Letters 148 (2024): 108871. https://doi.org/10.1016/j.chaos.2025.116856

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.

Publication Title

Chaos, Solitons & Fractals

DOI

10.1016/j.chaos.2025.116856