Numerical solving of dissipative solitons and Turing patterns in the Lugiato-Lefever equation using squared-operator iteration method

IF 2.2 3区物理与天体物理 Q2 OPTICS

Optics Communications Pub Date : 2025-06-26 DOI:10.1016/j.optcom.2025.132170

Gaoyan Cheng , Xiankun Yao

引用次数: 0

Abstract

This study develops the squared-operator iteration method to numerically solve dissipative solitons and Turing patterns in the Lugiato-Lefever equation. We analytically derive dissipative soliton solutions with a nonzero background and employ Fourier series expansion to obtain the discrete spectrum, along with the corresponding solutions of Turing patterns. These advances address a critical limitation of conventional squared-operator iteration method implementations. Linear stability analysis further examines the stability of these solutions under finite perturbations. Overall, this research provides an efficient and reliable approach for investigating nonlinear phenomena in the Lugiato-Lefever equation.

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用平方算子迭代法数值求解Lugiato-Lefever方程中的耗散孤子和图灵模式

本文发展了对Lugiato-Lefever方程中的耗散孤子和图灵模式进行数值求解的平方算子迭代方法。我们解析导出了具有非零背景的耗散孤子解，并利用傅里叶级数展开得到了离散谱，以及相应的图灵模式解。这些进展解决了传统的平方算子迭代方法实现的一个关键限制。线性稳定性分析进一步检验了这些解在有限扰动下的稳定性。总的来说，本研究为研究Lugiato-Lefever方程的非线性现象提供了一种有效而可靠的方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Optics Communications 物理-光学

CiteScore

5.10

自引率

8.30%

发文量

681

审稿时长

38 days

期刊介绍： Optics Communications invites original and timely contributions containing new results in various fields of optics and photonics. The journal considers theoretical and experimental research in areas ranging from the fundamental properties of light to technological applications. Topics covered include classical and quantum optics, optical physics and light-matter interactions, lasers, imaging, guided-wave optics and optical information processing. Manuscripts should offer clear evidence of novelty and significance. Papers concentrating on mathematical and computational issues, with limited connection to optics, are not suitable for publication in the Journal. Similarly, small technical advances, or papers concerned only with engineering applications or issues of materials science fall outside the journal scope.