Integrating analytical and numerical methods for studying the MGBF model's complex dynamics

Abstract

This study presents an in-depth analytical examination of the modified generalized Burgers-Fisher (MGBF) equation, emphasizing its intrinsic mathematical properties and multifaceted applications in hydrodynamics and signal analysis. The equation, which shares structural similarities with classical Burgers and Fisher formulations, exhibits distinct nonlinear characteristics that warrant comprehensive exploration. By employing advanced mathematical frameworks, specifically the modified Khater (MKhat) methodology and the unified formulation (UF) approach, this analysis derives exact analytical solutions to the governing equations.

The validation protocol incorporates He's variational iteration (HVI) technique, providing a rigorous numerical benchmark for evaluating the accuracy and stability of the obtained analytical solutions. Notably, the equation's capacity to model intricate nonlinear dynamics, including solitary wave propagation and deterministic chaos, undergoes meticulous mathematical scrutiny. The strong agreement between computational and analytical outcomes substantiates the mathematical robustness of the employed methodological framework.

The significance of this investigation extends beyond theoretical mathematics, offering valuable insights into the fundamental behavior of nonlinear evolutionary systems and their real-world applications in engineering and applied sciences. The findings establish a comprehensive theoretical foundation for advancing future research on nonlinear wave phenomena, stability analysis, and engineering implementations.