Study the dynamic behavior of bifurcation, chaos, time series analysis and soliton solutions to a Hirota model

The unified technique is a direct method that is employed in this study to extract a wide range of accurate solutions of the (2+1)-dimensional Hirota model. The governing model is frequently used in plasma physics to indicate the communications of evolving waves, to simulate the propagation of femtosecond and in nonlinear optical fiber. The main goal of this study is to investigate the novel technique that offers a more implemented and efficient handling of the nonlinear wave equation processes. Additionally, each of the determined solutions has a unique structure, including trigonometric, rational and hyperbolic. Also for the phase plane analysis, study the behavior of chaos, bifurcation and time series to the governing model. To demonstrate the behavior of traveling wave solutions and phase plane analysis, some of them are presented in 3-D, 2-D and density plots using Mathematica 11.0 and Matlab techniques of rk4 and ode45. The suggested methodology is very evident and easy to understand, yet effective and capable of introducing several types of solutions in a single framework. The determined results validate the unified technique’s ability to resolve other challenging nonlinear equations. Our research goes beyond the boundaries of theory and has potential applications in plasma physics, fluid dynamics, and nonlinear optics. The study elevates the understanding of complex systems in the field by offering new techniques.