AUTHOR=Pan Changchang , Wu Gangzhou , Bao Rui , Shao Boyun , Zhang Huicong 

TITLE=The rule for the number of fundamental Peregrine solitons involving multiple rogue wave states in the vector Chen-Lee-Liu nonlinear Schrödinger equation

JOURNAL=Frontiers in Physics

VOLUME=Volume 13 - 2025

YEAR=2025

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2025.1649398

DOI=10.3389/fphy.2025.1649398

ISSN=2296-424X

ABSTRACT=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.