  The stationary nonlinear Schroedinger equation, or Gross-Pitaevskii equation,
is studied for the cases of a single delta potential and a delta-shell
potential. These model systems allow analytical solutions, and thus provide
useful insight into the features of stationary bound, scattering and resonance
states of the nonlinear Schroedinger equation. For the single delta potential,
the influence of the potential strength and the nonlinearity is studied as well
as the transition from bound to scattering states. Furthermore, the properties
of resonance states for a repulsive delta-shell potential are discussed.
