Kopçasız Bahadır, Sağlam Fatma Nur Kaya, Emadifar Homan, Ahmed Karim K
Department of Computer Engineering, Faculty of Engineering and Architecture, Istanbul Gelisim University, Istanbul, Türkiye.
Department of Information Security Technology, Faculty of Computer and Information Technologies, Cappadocia University, Nevşehir, Türkiye.
Sci Rep. 2025 Jul 29;15(1):27617. doi: 10.1038/s41598-025-13193-y.
In this paper, the fascinating realm of the nonlinear coupled Kraenkel-Manna-Merle system is investigated. The proposed system is an effective tool used in the propagation of ferromagnetic particles in ferrite materials to realistically represent many nonlinear dynamic mechanisms in various scientific and engineering fields. First, a suitable wave transformation is applied to convert the nonlinear partial differential equation (NLPDE) into an ordinary differential equation (ODE). The next step, the Kumar-Malik method, and the new extended hyperbolic function method (nEHFM) are used to derive exact soliton solutions of the nonlinear coupled Kraenkel-Manna-Merle system. Using the offered procedures, many new soliton solutions, including Jacobi elliptic, hyperbolic, trigonometric, exponential, bright, dark, periodic, and some other singular soliton solutions, are obtained. The novelty of the solutions obtained is significant for the proposed paper. To provide a comprehensive visualization of the soliton dynamics, some of the solutions obtained are presented visually through graphical simulations of 3D, contour, and 2D plots. The outcomes of this study are novel and haven't been investigated for the main problem before. The results show that these methods are dependable, simple to use, and effective when analyzing different nonlinear models that are encountered in mathematical sciences and engineering. All solutions obtained are checked one by one with the Maple package program.
本文研究了非线性耦合Kraenkel-Manna-Merle系统这一引人入胜的领域。所提出的系统是一种有效的工具，用于铁磁颗粒在铁氧体材料中的传播，以真实地描述各种科学和工程领域中的许多非线性动力学机制。首先，应用适当的波变换将非线性偏微分方程（NLPDE）转换为常微分方程（ODE）。接下来，使用Kumar-Malik方法和新的扩展双曲函数方法（nEHFM）来推导非线性耦合Kraenkel-Manna-Merle系统的精确孤子解。通过所提供的过程，获得了许多新的孤子解，包括雅可比椭圆、双曲、三角、指数、亮、暗、周期以及其他一些奇异孤子解。所获得的解的新颖性对本文具有重要意义。为了全面可视化孤子动力学，通过3D、等高线和2D图的图形模拟直观地展示了所获得的一些解。本研究的结果是新颖的，之前尚未针对主要问题进行过研究。结果表明，这些方法在分析数学科学和工程中遇到的不同非线性模型时是可靠的、易于使用且有效的。所有获得的解都通过Maple软件包程序逐一进行了检验。
