Davey–Stewartson equation

In fluid dynamics, the Davey–Stewartson equation (DSE) was introduced in a paper by A. Davey and Keith Stewartson to describe the evolution of a three-dimensional wave-packet on water of finite depth. It is a system of partial differential equations for a complex (wave-amplitude) field A {\displaystyle A\,} and a real (mean-flow) field B {\displaystyle B} : i ∂ A ∂ t + c 0 ∂ 2 A ∂ x 2 + ∂ A ∂ y 2 = c 1 | A | 2 A + c 2 A ∂ B ∂ x , {\displaystyle i{\frac {\partial A}{\partial t}}+c_{0}{\frac {\partial ^{2}A}{\partial x^{2}}}+{\frac {\partial A}{\partial y^{2}}}=c_{1}|A|^{2}A+c_{2}A{\frac {\partial B}{\partial x}},} ∂ B ∂ x 2 + c 3 ∂ 2 B ∂ y 2 = ∂ | A | 2 ∂ x .

Source: Wikipedia — Davey–Stewartson equation (CC BY-SA 4.0)