Schrodinger-Poisson system

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The Schrodinger-Poisson system

i v^+_t + \Delta v/2 = u v^+ \,
i v^-_t - \Delta v/2 = u v^- \,
\Delta u = - |v^+|^2 + |v^-|^2\,

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

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