Khater Mostafa M A, Alfalqi Suleman H
School of Medical Informatics and Engineering, Xuzhou Medical University, 209 Tongshan Road, Xuzhou, 221004, Jiangsu, People's Republic of China.
Department of Basic Science, Obour High Institute for Engineering and Technology, Cairo, 11828, Egypt.
Sci Rep. 2024 Jul 30;14(1):17562. doi: 10.1038/s41598-024-68051-0.
This study investigates the nonlinear Pochhammer-Chree equation, a model crucial for understanding wave propagation in elastic rods, through the application of the Khater III method. The research aims to derive precise analytical solutions and validate them using He's variational iteration method (VIM). The Pochhammer-Chree equation's relationship to other nonlinear evolution equations, such as the Korteweg-de Vries and nonlinear Schrödinger equations, underscores its significance in the field of nonlinear wave dynamics. The methodology employs the Khater III method for deriving analytical solutions, while He's VIM serves as a numerical validation tool, ensuring the accuracy and stability of the obtained results. This dual approach not only yields novel solutions but also provides a robust framework for analyzing complex wave phenomena in elastic media. The findings of this study have significant implications for material science and engineering applications, offering new insights into the behavior of waves in elastic rods. By bridging the gap between theoretical models and practical applications, this research contributes to the advancement of both mathematical theory and physical understanding of nonlinear wave dynamics. Situated within the domain of applied mathematics, with a focus on nonlinear wave equations, this work exemplifies the interdisciplinary nature of contemporary research in mathematical physics. The results presented herein open new avenues for future investigations in related fields and highlight the potential for innovative applications in material science and engineering.
本研究通过应用卡特三世方法，对非线性泊松 - 克里方程进行了研究，该方程是理解弹性杆中波传播的关键模型。研究旨在推导精确的解析解，并使用何氏变分迭代法（VIM）对其进行验证。泊松 - 克里方程与其他非线性演化方程（如科特韦格 - 德弗里斯方程和非线性薛定谔方程）的关系，凸显了其在非线性波动动力学领域的重要性。该方法采用卡特三世方法推导解析解，而何氏VIM作为数值验证工具，确保所得结果的准确性和稳定性。这种双重方法不仅产生了新的解，还为分析弹性介质中的复杂波现象提供了一个强大的框架。本研究的结果对材料科学和工程应用具有重要意义，为弹性杆中波的行为提供了新的见解。通过弥合理论模型与实际应用之间的差距，本研究为非线性波动动力学的数学理论和物理理解的进步做出了贡献。这项工作位于应用数学领域，专注于非线性波动方程，体现了当代数学物理研究的跨学科性质。本文给出的结果为相关领域的未来研究开辟了新途径，并突出了材料科学和工程中创新应用的潜力。
