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

${\displaystyle i\partial _{t}^{}u+\nabla ^{2}u=un}$

${\displaystyle \Box n=-\nabla ^{2}(|u|_{}^{2})}$