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
The corresponding Lax representation for it is given in Boiti, Martina & Pempinelli (1995).
On the other hand, the equivalent counterpart of the DSE is the Ishimori equation.
The DSE is the result of a multiple-scale analysis of modulated nonlinear surface gravity waves, propagating over a horizontal sea bed.