fluid dynamics In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion ...

, the Davey–Stewartson equation (DSE) was introduced in a paper by A. Davey and

Keith Stewartson Keith Stewartson (20 September 1925 – 7 May 1983) was an English mathematician and fellow of the Royal Society. Early life The youngest of three children, Stewartson was born to an English baker in 1925. He was raised in Billingham, County Dur ...

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 Field may refer to: Expanses of open ground * Field (agriculture), an area of land used for agricultural purposes * Airfield, an aerodrome that lacks the infrastructure of an airport * Battlefield * Lawn, an area of mowed grass * Meadow, a grass ...

A\,

and a real ( mean-flow) field

B

: :

i \frac + c_0 \frac + \frac = c_1 , A, ^2 A + c_2 A\frac,

\frac + c_3 \frac = \frac.

The DSE is an example of a

soliton In mathematics and physics, a soliton is a nonlinear, self-reinforcing, localized wave packet that is , in that it preserves its shape while propagating freely, at constant velocity, and recovers it even after collisions with other such local ...

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 In theoretical physics, the (one-dimensional) nonlinear Schrödinger equation (NLSE) is a nonlinear variation of the Schrödinger equation. It is a classical field equation whose principal applications are to the propagation of light in nonli ...

i \frac + \frac + 2k , A, ^2 A =0.\,

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 Ishimori equation is a partial differential equation proposed by the Japanese mathematician . Its interest is as the first example of a nonlinear spin-one field model in the plane that is integrable . Equation The Ishimori equation has the for ...

. The DSE is the result of a

multiple-scale analysis In mathematics and physics, multiple-scale analysis (also called the method of multiple scales) comprises techniques used to construct uniformly valid approximations to the solutions of perturbation problems, both for small as well as large values ...

modulated Signal modulation is the process of varying one or more properties of a periodic waveform in electronics and telecommunication for the purpose of transmitting information. The process encodes information in form of the modulation or message ...

nonlinear surface gravity waves, propagating over a horizontal sea bed.

References

* * *

External links

Davey-Stewartson_system
at the dispersive equations wiki. Partial differential equations Integrable systems Equations of fluid dynamics {{theoretical-physics-stub

See also

References

External links