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 and a real (mean-flow) field :
The DSE is an example of a soliton equation in 2+1 dimensions. The corresponding Lax representation for it is given in .
In 1+1 dimensions the DSE reduces to the nonlinear Schrödinger equation
Itself, the DSE is the particular reduction of the Zakharov–Schulman system. 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.
See also
Ginzburg–Landau equation
Nonlinear systems
Ishimori equation
References
External links
Davey-Stewartson_system at the dispersive equations wiki.