Kadomtsev–Petviashvili equation

Summary

The Kadomtsev–Petviashvili equation, or KP equation, is a nonlinear wave equation in two space variables $x$ and $y$. It extends the Korteweg–De Vries equation to waves that move mainly in the $x$ direction but vary slowly in the $y$ direction. It comes in two versions, KP-I and KP-II, which differ by the sign of the $u_{yy}$ term. Like the KdV equation it is completely integrable.