Zakharov system

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
 * $$\begin{align} i \partial_t^{} u + \nabla^2 u &= un\\

\Box n &= -\nabla^2 (|u|^2_{})\end{align}$$ where $$\Box$$ is the d'Alembert operator.