The dynamical perspective of soliton solutions, bifurcation, chaotic and sensitivity analysis to the (3+1)-dimensional Boussinesq model

Muhammad Nadeem; Asad Islam; Mehmet Şenol; Yahya Alsayaad

doi:10.1038/s41598-024-59832-8

The dynamical perspective of soliton solutions, bifurcation, chaotic and sensitivity analysis to the (3+1)-dimensional Boussinesq model

Sci Rep. 2024 Apr 22;14(1):9173. doi: 10.1038/s41598-024-59832-8.

Authors

Muhammad Nadeem¹, Asad Islam², Mehmet Şenol³, Yahya Alsayaad⁴

Affiliations

¹ School of Mathematics and Statistics, Qujing Normal University, Qujing, 655011, China. nadeem@mail.qjnu.edu.cn.
² Department of Mechanical and Aerospace Engineering, Air University, Islamabad, Pakistan.
³ Department of Mathematics, Nevşehir Hacı Bektaş Veli University, Nevşehir, Turkey.
⁴ Department of Physics, Hodeidah University, Al-Hudaydah, Yemen. yahyaalsayyad2022@hoduniv.net.ye.

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.

Keywords: (3+1)-dimensional Boussinesq model; Bifurcation analysis; Chaotic structures; Exact soliton solutions; Quasi-periodic structures; Sensitivity analysis; Unified Riccati equation expansion method.