Nonlinear Partial Differential Equation

A nonlinear partial differential equation is a partial differential equation whose dependence on the unknown function or its derivatives does not define a linear operator. For example, the inviscid Burgers' equation is

The superposition principle therefore does not generally apply. Nonlinear partial differential equations are commonly classified as semilinear, quasilinear, or fully nonlinear according to the way their highest-order derivatives occur. Other examples include the Monge-Ampère equation and the Navier-Stokes equations (Evans 2010).