Английская Википедия: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 <math>A\,</math> and a real (mean-flow) field <math>B</math>:
- <math>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},</math>
- <math>\frac{\partial B}{\partial x^2} + c_3 \frac{\partial^2 B}{\partial y^2} = \frac{\partial |A|^2}{\partial x}.</math>
The DSE is an example of a soliton equation in 2+1 dimensions. The corresponding Lax representation for it is given in Шаблон:Harvtxt.
In 1+1 dimensions the DSE reduces to the nonlinear Schrödinger equation
- <math>i \frac{\partial A}{\partial t} + \frac{\partial^2 A}{\partial x^2} + 2k |A|^2 A =0.\,</math>
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
References
External links
- Davey-Stewartson_system at the dispersive equations wiki.
Шаблон:Theoretical-physics-stub
