Kadomtsev–Petviashvili equation

In mathematics and physics, the Kadomtsev–Petviashvili equation (often abbreviated as KP equation) is a partial differential equation to describe nonlinear wave motion. Named after Boris Borisovich Kadomtsev and Vladimir Iosifovich Petviashvili, the KP equation is usually written as ∂ x ( ∂ t u + u ∂ x u + ϵ 2 ∂ x x x u ) + λ ∂ y y u = 0 {\displaystyle \displaystyle \partial _{x}(\partial _{t}u+u\partial _{x}u+\epsilon ^{2}\partial _{xxx}u)+\lambda \partial _{yy}u=0} where λ = ± 1 {\displaystyle \lambda =\pm 1} .

Source: Wikipedia — Kadomtsev–Petviashvili equation (CC BY-SA 4.0)