Khater Mostafa M A, Alfalqi Suleman H, Vokhmintsev Aleksander
School of Medical Informatics and Engineering, Xuzhou Medical University, 209 Tongshan Road, 221004, Xuzhou, Jiangsu Province, P. R. China.
Institute of Digital Economy, Ugra State University, Khanty-Mansiysk, 628012, Russia.
Sci Rep. 2025 Feb 1;15(1):4013. doi: 10.1038/s41598-025-85263-0.
This study investigates the analytical solutions of a nonlinear evolution model governing the dynamics of graphene sheets, a material renowned for its exceptional electronic properties and versatile applications in nanotechnology. Three advanced analytical approaches-the Khater II (Khat II) method, the Khater III (Khat III) method, and the Generalized Rational (GRat) approach-are employed to derive exact solutions for this model with high precision. The accuracy and reliability of these solutions are validated by comparing them to numerical results obtained via He's Variational Iteration (HVI) method, which serves as a benchmark for numerical verification. The analysis reveals a remarkable agreement between the analytical and numerical solutions, highlighting the robustness and effectiveness of the proposed methodologies. Furthermore, this study provides new insights into the nonlinear dynamics and physical properties of graphene sheets, while also identifying connections to other prominent nonlinear evolution equations. The innovative use of these analytical techniques offers practical frameworks for addressing complex nonlinear models in mathematical physics, thus advancing solution methodologies for such equations. This research contributes significantly to applied mathematics, material science, and nanotechnology by delivering accurate solutions and enhancing our understanding of graphene's nonlinear behavior. Finally, the findings have far-reaching implications, offering potential applications in designing advanced materials with tailored properties to support technological advancements, thereby pushing the boundaries of nanotechnology and materials engineering.
本研究探讨了一个非线性演化模型的解析解，该模型描述了石墨烯片的动力学，石墨烯是一种以其卓越的电子特性和在纳米技术中的广泛应用而闻名的材料。采用了三种先进的解析方法——哈特二世（Khat II）方法、哈特三世（Khat III）方法和广义有理（GRat）方法——来高精度地推导该模型的精确解。通过将这些解与通过何氏变分迭代（HVI）方法获得的数值结果进行比较，验证了这些解的准确性和可靠性，HVI方法作为数值验证的基准。分析表明解析解与数值解之间具有显著的一致性，突出了所提出方法的稳健性和有效性。此外，本研究为石墨烯片的非线性动力学和物理性质提供了新的见解，同时还确定了与其他著名非线性演化方程的联系。这些解析技术的创新性应用为解决数学物理中的复杂非线性模型提供了实用框架，从而推进了此类方程的求解方法。这项研究通过提供精确解并加深我们对石墨烯非线性行为的理解，对应用数学、材料科学和纳米技术做出了重大贡献。最后，研究结果具有深远的意义，为设计具有定制特性的先进材料以支持技术进步提供了潜在应用，从而推动了纳米技术和材料工程的发展。
