In mathematics, the Zakharov system is a system of non-linear partial differential equations, introduced by
Vladimir Zakharov in 1972 to describe the propagation of
Langmuir wave
Langmuir may refer to:
* Langmuir (crater), an impact crater on the Moon's far side
* ''Langmuir'' (journal), an academic journal on colloids, surfaces and interfaces, published by the American Chemical Society
* Langmuir (unit), a unit of expos ...
s in an
ionized
Ionization, or Ionisation is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged atom or molecule ...
plasma
Plasma or plasm may refer to:
Science
* Plasma (physics), one of the four fundamental states of matter
* Plasma (mineral), a green translucent silica mineral
* Quark–gluon plasma, a state of matter in quantum chromodynamics
Biology
* Blood pla ...
. The system consists of a complex field ''u'' and a real field ''n'' satisfying the equations
:
:
See also
*
Resonant interaction
In nonlinear systems, a resonant interaction is the interaction of three or more waves, usually but not always of small amplitude. Resonant interactions occur when a simple set of criteria coupling wave-vectors and the dispersion equation are met ...
; the Zakharov equation describes non-linear resonant interactions.
References
* Zakharov, V. E. (1968). ''Stability of periodic waves of finite amplitude on the surface of a deep fluid.'' Journal of Applied Mechanics and Technical Physics, 9(2), 190-194.
*.
Partial differential equations
Waves in plasmas
Plasma physics
Gravity waves
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