Nonlinear analysis is a branch of mathematics that focuses on systems where the output is not directly proportional to the input. Unlike linear systems, where changes are predictable and follow a straight line, nonlinear systems can exhibit complex behaviors such as chaos, bifurcations, and multiple equilibria. This makes them essential for understanding real-world phenomena in fields like physics, engineering, and economics. In nonlinear analysis, various techniques are employed to study these complex systems, including differential equations, fixed-point theorems, and variational methods. Researchers use these tools to analyze stability, control, and optimization in systems that cannot be easily described by linear models. This area of study is crucial for advancing technology and improving decision-making processes in various disciplines.