Some exact solutions of the Schr\"odinger--Poisson system in spaces of constant sectional curvature
Abstract
We consider the Schr\"odinger--Poisson system on the complete, simply-connected Riemannian manifolds of constant sectional curvature. We obtain closed-form stationary spherically-symmetric solutions for the homogeneous equations for certain dimensions, and give some basic examples of solutions with a nonzero background.
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