Nadeem Muhammad, Islam Asad, Şenol Mehmet, Alsayaad Yahya
School of Mathematics and Statistics, Qujing Normal University, Qujing, 655011, China.
Department of Mechanical and Aerospace Engineering, Air University, Islamabad, Pakistan.
Sci Rep. 2024 Apr 22;14(1):9173. doi: 10.1038/s41598-024-59832-8.
In this study, we examine multiple perspectives on soliton solutions to the (3+1)-dimensional Boussinesq model by applying the unified Riccati equation expansion (UREE) approach. The Boussinesq model examines wave propagation in shallow water, which is derived from the fluid dynamics of a dynamical system. The UREE approach allows us to derive a range of distinct solutions, such as single, periodic, dark, and rational wave solutions. Furthermore, we present the bifurcation, chaotic, and sensitivity analysis of the proposed model. We use planar dynamical system theory to analyze the structure and characteristics of the system's phase portraits. The current study depends on a dynamic structure that has novel and unexplored results for this model. In addition, we display the behaviors of associated physical models in 3-dimensional, density, and 2-dimensional graphical structures. Our findings demonstrate that the UREE technique is a valuable mathematical tool in engineering and applied mathematics for studying wave propagation in nonlinear evolution equations.
在本研究中，我们通过应用统一的里卡蒂方程展开法（UREE），考察了关于（3 + 1）维布辛涅斯克模型孤子解的多个视角。布辛涅斯克模型研究浅水波传播，它源自一个动力系统的流体动力学。UREE方法使我们能够推导出一系列不同的解，如单波、周期波、暗波和有理波解。此外，我们给出了所提出模型的分岔、混沌和敏感性分析。我们使用平面动力系统理论来分析系统相图的结构和特征。当前的研究依赖于一种动态结构，该结构对于此模型具有新颖且未被探索的结果。此外，我们在三维、密度和二维图形结构中展示了相关物理模型的行为。我们的研究结果表明，UREE技术是工程学和应用数学中用于研究非线性演化方程中波传播的一种有价值的数学工具。
