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通过两种不同方法得到的非线性光学中出现的时间分数阶阿克博塔方程的光学解。

Optical solutions to the time fractional Akbota equation arising in nonlinear optics via two distinct methods.

作者信息

Mahmood Salim S, Boulaaras Salah Mahmoud, Murad Muhammad Amin S, Malik Sandeep

机构信息

Department of Mathematics, Faculty of Science, Soran University, Erbīl, Iraq.

Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia.

出版信息

Sci Rep. 2025 Aug 6;15(1):28823. doi: 10.1038/s41598-025-14719-0.

DOI:10.1038/s41598-025-14719-0
PMID:40770060
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC12328652/
Abstract

This paper investigates the optical soliton solutions of the time-fractional Akbota equation, a model arising in nonlinear optics. The generalized rational function method and the F-expansion approach are utilized to derive soliton solutions incorporating the beta-derivative. These solutions are depicted through 2D, contour, and 3D graphical representations, illustrating the temporal evolution of soliton profiles and revealing the influence of the fractional parameter β on soliton dynamics. The impact of the conformable derivative parameter and time on the optical solutions is also analyzed, emphasizing their role in shaping soliton properties. The graphical studies highlight the stability and propagation characteristics of solitons, offering valuable insights into their behavior under varying parameters. This research contributes to a deeper understanding of the Akbota equation, enhancing its application in surface geometry and aiding in the development of advanced models for optical and magnetic phenomena in nonlinear systems.

摘要

本文研究了时间分数阶阿克博塔方程的光学孤子解，该方程是一个出现在非线性光学中的模型。利用广义有理函数方法和F展开法推导了包含β导数的孤子解。通过二维、等高线和三维图形表示对这些解进行了描绘，展示了孤子轮廓的时间演化，并揭示了分数参数β对孤子动力学的影响。还分析了共形导数参数和时间对光学解的影响，强调了它们在塑造孤子特性中的作用。图形研究突出了孤子的稳定性和传播特性，为其在不同参数下的行为提供了有价值的见解。这项研究有助于更深入地理解阿克博塔方程，增强其在表面几何中的应用，并有助于开发非线性系统中光学和磁现象的高级模型。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8479/12328652/41a1f26ff7ab/41598_2025_14719_Fig11_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8479/12328652/c1d2b65574cf/41598_2025_14719_Fig1_HTML.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8479/12328652/dbf7bc233b13/41598_2025_14719_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8479/12328652/e712ccbd930d/41598_2025_14719_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8479/12328652/77fc65bbc49c/41598_2025_14719_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8479/12328652/099aac02e1a2/41598_2025_14719_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8479/12328652/713e9c470757/41598_2025_14719_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8479/12328652/70a62b5a63e0/41598_2025_14719_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8479/12328652/b749b5c42753/41598_2025_14719_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8479/12328652/42567eb78f8b/41598_2025_14719_Fig10_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8479/12328652/41a1f26ff7ab/41598_2025_14719_Fig11_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8479/12328652/c1d2b65574cf/41598_2025_14719_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8479/12328652/ed4ca41a02d6/41598_2025_14719_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8479/12328652/dbf7bc233b13/41598_2025_14719_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8479/12328652/e712ccbd930d/41598_2025_14719_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8479/12328652/77fc65bbc49c/41598_2025_14719_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8479/12328652/099aac02e1a2/41598_2025_14719_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8479/12328652/713e9c470757/41598_2025_14719_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8479/12328652/70a62b5a63e0/41598_2025_14719_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8479/12328652/b749b5c42753/41598_2025_14719_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8479/12328652/42567eb78f8b/41598_2025_14719_Fig10_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8479/12328652/41a1f26ff7ab/41598_2025_14719_Fig11_HTML.jpg

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本文引用的文献

1
Soliton solutions to the generalized derivative nonlinear Schrödinger equation under the effect of multiplicative white noise and conformable derivative.乘性白噪声和一致导数作用下广义导数非线性薛定谔方程的孤子解
Sci Rep. 2025 Jun 4;15(1):19599. doi: 10.1038/s41598-025-04981-7.
2
Bifurcation, chaotic behaviors and solitary wave solutions for the fractional Twin-Core couplers with Kerr law non-linearity.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
Sci Rep. 2024 Sep 30;14(1):22616. doi: 10.1038/s41598-024-74044-w.
3
Exact analytical soliton solutions of the M-fractional Akbota equation.
M-分数阶阿克博塔方程的精确解析孤子解
Sci Rep. 2024 Jun 11;14(1):13360. doi: 10.1038/s41598-024-64328-6.