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利用M截断分数阶导数的流体动力学非线性复方程中的一些新型光脉冲。

Some novel optical pulses in hydrodynamical nonlinear complex equation using M-truncated fractional derivative.

作者信息

Ilhan Esin, Rehman Shafqat Ur, Bilal Muhammad, Baskonus Haci Mehmet, Alawaideh Yazen M

机构信息

Faculty of Engineering and Architecture, Kirsehir Ahi Evran University, Kirsehir, Turkey.

Department of Mathematics, Grand Asian University, Sialkot, 51310, Pakistan.

出版信息

Sci Rep. 2025 Sep 1;15(1):32139. doi: 10.1038/s41598-025-17423-1.

DOI:10.1038/s41598-025-17423-1
PMID:40890224
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC12402286/
Abstract

This study investigates soliton solutions and dynamic wave structures in the complex Ginzburg-Landau (CGL) equation, which is crucial for understanding wave propagation in various physical systems. We employ three analytical methods: the Kumar-Malik method, the generalized Arnous method, and the energy balance method to derive novel closed-form solutions. These solutions exhibit diverse solitonic phenomena, including multi-wave solitons, complex solitons, singular solitons, periodic oscillating waves, dark-wave, and bright-wave profiles. Our results reveal new families of exact solitary waves via the generalized Arnous method and diverse soliton solutions through the Kumar-Malik method, including hyperbolic, trigonometric, and Jacobi elliptic functions. Verification is ensured through back-substitution to the considered model using Mathematica software. Additionally, we plot the various graphs with the appropriate parametric values under the influence of the M-truncated fractional derivative to visualize the solution behaviors with varying parameter values. This research contributes significantly to understanding wave dynamics in physical oceanography, and the unique outcomes explored in this research will play a vital role for the forthcoming investigation of nonlinear equations.

摘要

本研究探讨复金兹堡 - 朗道（CGL）方程中的孤子解和动态波结构，这对于理解各种物理系统中的波传播至关重要。我们采用三种解析方法：库马尔 - 马利克方法、广义阿诺方法和能量平衡方法来推导新的闭式解。这些解展现出多样的孤子现象，包括多波孤子、复孤子、奇异孤子、周期振荡波、暗波和亮波剖面。我们的结果通过广义阿诺方法揭示了新的精确孤立波族，并通过库马尔 - 马利克方法得到了多样的孤子解，包括双曲函数、三角函数和雅可比椭圆函数。使用Mathematica软件通过将结果代回所考虑的模型进行验证。此外，我们在M - 截断分数阶导数的影响下，绘制了具有适当参数值的各种图形，以可视化不同参数值下的解行为。本研究对理解物理海洋学中的波动动力学有显著贡献，并且本研究中探索的独特成果将对即将开展的非线性方程研究发挥重要作用。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9784/12402286/092c6701f169/41598_2025_17423_Fig16_HTML.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9784/12402286/092c6701f169/41598_2025_17423_Fig16_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9784/12402286/596c5e7f1a92/41598_2025_17423_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9784/12402286/0ab9ff5fcb0d/41598_2025_17423_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9784/12402286/6dcc1120e04f/41598_2025_17423_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9784/12402286/329e6c0a08bf/41598_2025_17423_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9784/12402286/f6b19a7b02ad/41598_2025_17423_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9784/12402286/cc7cb383d973/41598_2025_17423_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9784/12402286/45c59eb60118/41598_2025_17423_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9784/12402286/50284b51d969/41598_2025_17423_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9784/12402286/1a3fdf63026f/41598_2025_17423_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9784/12402286/d7581efa365c/41598_2025_17423_Fig10_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9784/12402286/e0906f931796/41598_2025_17423_Fig11_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9784/12402286/80a2111f2211/41598_2025_17423_Fig12_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9784/12402286/34734a8f2390/41598_2025_17423_Fig13_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9784/12402286/f20cf9749802/41598_2025_17423_Fig14_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9784/12402286/d472002542a3/41598_2025_17423_Fig15_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9784/12402286/092c6701f169/41598_2025_17423_Fig16_HTML.jpg

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