# Schrodinger-Poisson system

The Schrodinger-Poisson system

${\displaystyle iv_{t}^{+}+\Delta v/2=uv^{+}\,}$
${\displaystyle iv_{t}^{-}-\Delta v/2=uv^{-}\,}$
${\displaystyle \Delta u=-|v^{+}|^{2}+|v^{-}|^{2}\,}$

arises as the non-relativistic limit of the nonlinear Klein-Gordon equation.