Lie symmetries, soliton dynamics, bifurcation analysis and chaotic behavior in the reduced Ostrovsky equation

This article studies the reduced Ostrovsky equation by using Lie group theory, an efficient method for deriving symmetries in nonlinear equations. The method starts by finding infinitesimal generators and then adjoint and commutator tables are constructed to explore the relationships between the generators. The optimal system of solutions is then determined which leads the reduction of the partial differential equation into a simple ordinary differential equation. To find explicit solutions, the extended hyperbolic function method is applied. This yields various soliton solutions, including dark solitons, bright solitons, singular solitons, and periodic-singular solitons. The physical behavior of these solitons is further illustrated through 3D and 2D plots, which help visualize how the parameter constraints affect the solutions. The model is also subjected to a qualitative analysis, exploring bifurcation and chaotic behavior. Phase profiles are constructed using different values of parameters to show how the system can exhibit quasi-periodic and chaotic dynamics, when an external periodic force is applied. Different tools are used to detect chaos such as 2d phase plots and time series plots to offer a deeper understanding of the system’s dynamics and parameter variations. Hence, this study not only gives explicit soliton solutions but also reveals the complex dynamics of the reduced Ostrovsky equation. We have now included the sensitivity analysis, which examines the influence of key parameters on the system’s dynamics, enhancing the understanding of the model’s chaotic behavior.