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Updated: Jun 28, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
The dynamical perspective of soliton solutions, bifurcation, chaotic and sensitivity analysis to the
Muhammad Nadeem1, Asad Islam2, Mehmet Şenol3
1School of Mathematics and Statistics, Qujing Normal University, Qujing, 655011, China. nadeem@mail.qjnu.edu.cn.
Abstract:
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.
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