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
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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).
