Nonlinear Partial Differential Equations

Nonlinear partial differential equations (PDEs) are mathematical formulas that describe how complex systems change across space and time, where the relationship involves multiple variables. "Nonlinear" means the relationship isn't straightforward—small changes can lead to big differences, and solutions can be unpredictable or exhibit intricate behaviors like waves or chaos. These equations are used to model phenomena such as weather patterns, fluid flow, and biological systems, helping us understand and predict their behavior despite their complexity.