### Hellenica World

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 plasma. The system consists of a complex field u and a real field n satisfying the equations

$$i \partial_t^{} u + \nabla^2 u = un$$
$$\Box n = -\nabla^2 (|u|^2_{})$$

NAKANISHI Kenji - Wellposedness and scattering for the Zakharov system in four dimensions

References

Zakharov, V. E. (1972), "Collapse of Langmuir waves", Soviet Journal of Experimental and Theoretical Physics 35: 908–914, Bibcode 1972JETP...35..908Z.