The study of wave propagation for (2 + 1)-dimensional Bogoyavlenskii’s breaking soliton system

An important aspect of the study of nonlinear processes is the examination of integrable nonlinear evolution equations. This paper concerns propagation phenomena for the integrable (2 + 1)-dimensional Bogoyavlenskii’s breaking soliton equation. We employ the Bernoulli sub-ODE approach to find travelling wave solutions for these integrable nonlinear systems. The findings demonstrate that the model used in this study provides various explicit travelling wave solutions. We also examine how the parameters of the solutions affect the wave propagation speed. Suitable parameter values are selected to depict the obtained explicit soliton solutions graphically. In 2D and 3D graphs, the behaviour of the solitary wave patterns is shown. Additionally, an in-depth examination of the stability properties of the system is undertaken, employing bifurcation analysis techniques to elucidate the behaviour of the system under varying parameter values. Moreover, the research delves into the construction of phase portraits, allowing for a comprehensive visualization of the dynamics, while concurrently presenting analytical solutions for the planar system being investigated. Furthermore, the study employs rigorous mathematical methods to explore the bifurcation behaviour of the breaking soliton equation, enabling a thorough understanding of complex dynamical characteristics, with a focus on their phase portraits and associated solutions. To ensure the accuracy of the obtained solutions, we performed a validation process using Maple software, where we reintroduced the solutions back into their respective original equations.