|本期目录/Table of Contents|

[1]陈昌娣,徐映红.(2+1)维复Ginzburg Landau方程的有限差分法及稳定性分析[J].浙江理工大学学报,2025,53-54(自科三):432-441.
　CHEN Changdi,XU Yinghong.The finite difference method and stability analysis of a (2+1)  dimensional complex Ginzburg Landau equation[J].Journal of Zhejiang Sci-Tech University,2025,53-54(自科三):432-441.
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(2+1)维复Ginzburg Landau方程的有限差分法及稳定性分析()
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浙江理工大学学报[ISSN:1673-3851/CN:33-1338/TS]

卷:
第53-54卷
期数:
2025年自科第三期
页码:
432-441
栏目:
出版日期:
2025-05-05

文章信息/Info

Title:
The finite difference method and stability analysis of a (2+1)  dimensional complex Ginzburg Landau equation
文章编号:
1673-3851 (2025) 05-0432-10
作者:
陈昌娣; 徐映红
浙江理工大学理学院，杭州 310018
Author(s):
CHEN Changdi; XU Yinghong
School of Science, Zhejiang SciTech University, Hangzhou 310018, China
关键词:
GinzburgLandau方程; 数值模拟; 有限差分法; 傅里叶分析; 稳定性
分类号:
TS101; O242-1
文献标志码:
A
摘要:
以包含色散、光学滤波、非线性增益和线性增益项的(2+1)维复GinzburgLandau方程为研究对象，提出了求解该方程的有限差分格式，证明了方程解的有界性、差分格式的稳定性。首先，构造了求解该方程的有限差分格式，时间上采用二阶倒向微分格式，空间上采用中心差分格式，利用外推方法替代非线性项，从而得到一个二层非线性差分格式及其对应的交替方向隐格式。然后，利用傅里叶分析方法从理论上证明了该格式是无条件稳定的。最后，通过数值实验验证差分格式模拟孤子演化的有效性，并探究初始扰动和边界扰动对孤子演化的影响。结果表明：该差分格式是稳定的，且具有二阶精度；相比边界扰动，初始扰动对孤子演化的影响更大。该研究结果可丰富GinzburgLandau方程的理论研究，为研究Ginzburg Landau方程的参数确定反问题提供一定基础。

参考文献/References:

［1］Ginzburg V L, Landau L D. On the theory of superconductivity［M］∥ Ginzburg V L. On Superconductivity and Superfluidity: A Scientific Autobiography. Berlin, Heidelberg: Springer, 2009:113-137.
［2］Aranson I S, Kramer L. The world of the complex Ginzburg-Landau equation［J］. Reviews of Modern Physics, 2002, 74(1):99-143.
［3］Chang W, Ankiewicz A, Soto-Crespo J M, et al. Dissipative soliton resonances［J］. Physical Review A, 2008, 78(2):023830.
［4］Kraus M, Walter D, Michalowski A, et al. Processing techniques and system technology for precise and productive microdrilling in metals［J］. Springer Series in Optical Sciences, 2016, 195: 201-230.
［5］He Y J, Mihalache D. Lattice solitons in optical media described by the complex Ginzburg-Landau model with PT-symmetric periodic potentials［J］. Physical Review A, 2013, 87: 013812.
［6］Liu Y, Chen S Q, Wei L X, et al. Exact solutions to complex Ginzburg-Landau equation［J］. Pramana, 2018, 91(2): 29.
［7］Osman M S, Ghanbari B, Machado J A T. New complex waves in nonlinear optics based on the complex Ginzburg-Landau equation with Kerr law nonlinearity［J］. The European Physical Journal Plus, 2019, 134(1): 20.
［8］Yan Y Y, Liu W J. Soliton rectangular pulses and bound states in a dissipative system modeled by the variable-coefficients complex cubic-quintic Ginzburg-Landau equation［J］. Chinese Physics Letters, 2021, 38(9): 094201.
［9］胡艳,孙峪怀.应用多项式完全判别系统方法求解时空分数阶复Ginzburg-Landau方程［J］.应用数学和力学,2021,42(8):874-880.
［10］杨佳奇,刘文军.基于变系数3+1维三次-五次复金兹堡-朗道方程的亮孤子及混合孤子传输特性［J］. 物理学报, 2023, 72(10): 173-179.

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备注/Memo

备注/Memo:
收稿日期： 2023-02-22
网络出版日期：2023-09-08
基金项目： 国家自然科学基金项目(11501513,11471287)；浙江省自然科学基金项目(LY18A010030)
作者简介： 陈昌娣(1997—)，女，贵州贵阳人，硕士研究生，主要从事反问题理论及应用方面的研究
通信作者： 徐映红，E-mail：xyh7913@163.com
更新日期/Last Update: 2025-05-06