Zakharov System
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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 waves 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. The system consists of a complex field ''u'' and a real field ''n'' satisfying the equations :i \partial_t^ u + \nabla^2 u = un :\Box n = -\nabla^2 (, u, ^2_)


See also

* Resonant interaction; 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 {{plasma-stub