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 3;15(1):4101. doi: 10.1038/s41598-025-88096-z.
The primary objective of this study is to derive analytical solutions for a significant system that models the evolution of complex wave fields in nonlinear media. This system extends the framework of nonlinear Schrödinger equations and is pivotal in various physical applications, including optical fibers and Bose-Einstein condensates. By employing advanced analytical techniques such as the Khater II, III (Khat II, Khat III) and Unified (UF) methods, we successfully obtain exact analytical solutions that enhance our understanding of the system's dynamic behavior. The findings reveal a variety of soliton-like solutions, demonstrating the robustness and effectiveness of the methodologies employed. This research underscores the importance of the system in modeling intricate physical phenomena and offers a novel perspective on its solution space. The originality of this study lies in the innovative application of Khat II, Khat III, and UF methods to this system, providing valuable insights and methodologies for future research endeavors. This work represents a significant contribution to applied mathematics and nonlinear dynamics, emphasizing the physical relevance of the system in representing nonlinear wave interactions. The analytical solutions obtained can facilitate precise control and prediction of wave behaviors in practical applications, thereby advancing our capability to manipulate and harness nonlinear wave phenomena in diverse scientific and engineering contexts.
本研究的主要目标是为一个重要系统推导解析解，该系统对非线性介质中复杂波场的演化进行建模。此系统扩展了非线性薛定谔方程的框架，在包括光纤和玻色 - 爱因斯坦凝聚体在内的各种物理应用中起着关键作用。通过采用诸如卡特二世、三世（Khat II、Khat III）和统一（UF）方法等先进的分析技术，我们成功获得了精确的解析解，这加深了我们对系统动态行为的理解。研究结果揭示了多种类孤子解，证明了所采用方法的稳健性和有效性。这项研究强调了该系统在对复杂物理现象建模中的重要性，并为其解空间提供了新的视角。本研究的创新性在于将卡特二世、三世和UF方法创新性地应用于该系统，为未来的研究工作提供了有价值的见解和方法。这项工作对应用数学和非线性动力学做出了重大贡献，强调了该系统在表示非线性波相互作用方面的物理相关性。所获得的解析解有助于在实际应用中精确控制和预测波的行为，从而提高我们在各种科学和工程背景下操纵和利用非线性波现象的能力。
