Bifurcation and multi-stability analysis of microwave engineering systems: Insights from the Burger–Fisher equation

The present article depicts the research being done on the microwave effect realized by the often-used Burger–Fisher equation. A particular view is on the emergence of multi-stability and the bifurcations associated with microwave engineering systems. A novel rational, trigonometric, and hyperbolic form of the traveling waves is furnished by the resolution of the non-linear issue with the aid of the advanced exp $(-\Psi \left(\eta \right))$-expansion function parameterization. Firstly, we will solve the exact form of the Burger–Fisher equation, which clarifies the behavior of the equation in different conditions. Subsequently, bifurcation analysis techniques will be employed to study the nuanced relationship between the system parameters and the emergence of multistability phenomena. Through our results, we exposed the complicated essential features of microwave physics and established crucial parameters that determine a system’s behavior. Next, we cover control principle issues and practical applications in microwave engineering problems. This model accommodates the essential features of multi-stable dynamic systems and provides an important framework for creating microwave devices and circuits.The main aim of this research work is to analyze the phenomenon of multi-stability and bifurcation in microwave engineering systems by applying Burger–Fisher equation. The study intends to obtain new solutions to the PDEs through the application of a new method, the exp $(-\Psi \left(\eta \right))$-expansion function method that uses rational, trigonometric, and hyperbolic traveling wave solutions. Existing research of the Burger–Fisher equation is not explicit and by solving the exact form the research aims at exploring the different conditions under which the equation behaves and studying the delicate interactions between the parameters of the multistable system.