nonlinear PDEs

Nonlinear partial differential equations (PDEs) are mathematical formulas that describe how quantities like heat, waves, or fluids change both in space and time, where the relationship between the variables isn’t straightforward. Unlike linear PDEs, where changes follow direct, proportional rules, nonlinear PDEs involve interactions that can create complex behaviors such as turbulence or sharp edges. They are essential in modeling real-world phenomena where effects are interconnected and unpredictable, making their analysis more challenging but also more accurate for many physical, biological, and financial systems.