ORIGINAL RESEARCH article
Front. Phys.
Sec. Optics and Photonics
Volume 13 - 2025 | doi: 10.3389/fphy.2025.1649398
The rule for the number of fundamental Peregrine solitons involving multiple rogue wave states in the vector Chen-Lee-Liu nonlinear Schrödinger equation
Provisionally accepted
- 1Tongling University, Tongling, China
- 2Southeast University, Nanjing, China
- 3Zhejiang A and F University, Hangzhou, China
Select one of your emails
You have multiple emails registered with Frontiers:
Notify me on publication
Please enter your email address:
If you already have an account, please login
You don't have a Frontiers account ? You can register here
This study investigates the physical distribution patterns of Peregrine solitons within multi-order rogue wave states and their potential applications in optical systems under the vector Chen-Lee-Liu nonlinear Schrödinger equation framework. Through non-recursive Darboux transformation, we systematically analyze the nonlinear dynamics of vector optical fields during second-harmonic generation, revealing an arithmetic progression in Peregrine soliton evolution across rogue wave orders. For nth-order solutions, the fundamental Peregrine soliton count follows an arithmetic sequence with first term n(n -1), last term n(n + 1), and common difference n, where each rogue wave state comprises fully decoupled Peregrine solitons (e.g., 1/2 for 1st-order, 2/4/6 for 2nd-order, and 6/9/12 for 3rd-order configurations). It is noteworthy that the emergence of nonet rogue wave states (nine Peregrine solitons) in third-order solutions breaks through the conventional even-mode constraint in second-order solutions, opening new avenues for investigating many-body nonlinear interactions in multi-channel photonic devices. These findings provide significant insights into the spatiotemporal localization characteristics of rogue waves in multi-component nonlinear media and their applications in optical sensing and quantum information processing.
Keywords: Peregrine soliton, multiple rogue wave states, vector Chen-Lee-Liu system, Self-steepening, non-recursive Darboux transform
Received: 18 Jun 2025; Accepted: 08 Aug 2025.
Copyright: © 2025 Pan, Wu, Bao, Shao and Zhang. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence:
Changchang Pan, Tongling University, Tongling, China
Huicong Zhang, Zhejiang A and F University, Hangzhou, China
Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.