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具有克尔定律非线性的分数阶双芯耦合器的分岔、混沌行为和孤立波解

Bifurcation, chaotic behaviors and solitary wave solutions for the fractional Twin-Core couplers with Kerr law non-linearity.

作者信息

Li Zhao, Lyu Jingjing, Hussain Ejaz

机构信息

College of Computer Science, Chengdu University, Chengdu, 610106, People's Republic of China.

Key Laboratory of Numerical Simulation of Sichuan Provincial Universities, School of Mathematics and Information Sciences, Neijiang Normal Univeristy, Neijiang, 641000, Sichuan Province, People's Republic of China.

出版信息

Sci Rep. 2024 Sep 30;14(1):22616. doi: 10.1038/s41598-024-74044-w.

DOI:10.1038/s41598-024-74044-w
PMID:39349816
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC11443055/
Abstract

The main purpose of this article is to analyze the bifurcation, chaotic behaviors, and solitary wave solutions of the fractional Twin-Core couplers with Kerr law non-linearity by using the planar dynamical system method. This equation has profound physical significance and application value in the areas of optics and optical communication. Firstly, the traveling wave transformation is applied to convert the beta-derivative Twin-Core couplers with Kerr law non-linearity into the ordinary differential equations. Secondly, phase portraits and Poincaré sections of two-dimensional dynamical system and its perturbation system are plotted by using mathematical software. For different initial values, the planar phase diagram and three-dimensional phase diagram in red and blue are plotted, respectively. Finally, the solitary wave solutions of the fractional Twin-Core couplers with Kerr law non-linearity are obtained by using theory of planar dynamical system. In addition, three-dimensional graphs, two-dimensional graphs, and the contour graphs of the solitary wave solutions are drawn.

摘要

本文的主要目的是运用平面动力系统方法分析具有克尔定律非线性的分数阶双芯耦合器的分岔、混沌行为和孤立波解。该方程在光学和光通信领域具有深刻的物理意义和应用价值。首先，应用行波变换将具有克尔定律非线性的β导数双芯耦合器转化为常微分方程。其次，利用数学软件绘制二维动力系统及其摄动系统的相图和庞加莱截面。对于不同的初始值，分别绘制了红色和蓝色的平面相图和三维相图。最后，运用平面动力系统理论得到了具有克尔定律非线性的分数阶双芯耦合器的孤立波解。此外，还绘制了孤立波解的三维图、二维图和等高线图。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b10e/11443055/40cd6f4868f3/41598_2024_74044_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b10e/11443055/e689e408d110/41598_2024_74044_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b10e/11443055/2d0bebfe3069/41598_2024_74044_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b10e/11443055/e382d0c72452/41598_2024_74044_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b10e/11443055/ac7837619532/41598_2024_74044_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b10e/11443055/51498f854823/41598_2024_74044_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b10e/11443055/87e6663a510f/41598_2024_74044_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b10e/11443055/fbcb4333bf46/41598_2024_74044_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b10e/11443055/11e7169ca6e9/41598_2024_74044_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b10e/11443055/40cd6f4868f3/41598_2024_74044_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b10e/11443055/e689e408d110/41598_2024_74044_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b10e/11443055/2d0bebfe3069/41598_2024_74044_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b10e/11443055/e382d0c72452/41598_2024_74044_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b10e/11443055/ac7837619532/41598_2024_74044_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b10e/11443055/51498f854823/41598_2024_74044_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b10e/11443055/87e6663a510f/41598_2024_74044_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b10e/11443055/fbcb4333bf46/41598_2024_74044_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b10e/11443055/11e7169ca6e9/41598_2024_74044_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b10e/11443055/40cd6f4868f3/41598_2024_74044_Fig9_HTML.jpg

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