  Single channel, single energy partial wave analyses (SE_PWA) are from the
first principles non-unique in the inelastic region if only data from elastic
channels are used, so we in details discuss mechanisms how the problem is
eliminated in pion-nucleon scattering. The "continuum ambiguities" puzzle has
been extensively discussed since early 1970es, and two major mechanisms for
solving the problem have been suggested: either to ensure the continuity of
Argand diagrams by imposing the T-matrix t-channel analyticity
(Karlsruhe-Helsinki, VPI/GWU) or to restore the unitarity loss in the
kinematical regime where the inelastic channels are successively opened by
replacing the standard single channel PWA by the coupled channel formalism
(CMB, Zagreb, Kent, Pittsburgh/ANL, Giessen). In both approaches the
insufficiency of the single channel data is eliminated by introducing
additional constraints using the data from other channels. The importance and
physical meaning of the second approach is presented in details, and the
significance of inelastic channels for the uniqueness of the partial wave
analysis is discussed. The outline of the procedure for utilizing the coupled
channel formalism to perform the search for the minimal number/full set of
T-matrix poles in the complex energy plane, which connect the quark model
predictions to experimental reality, is proposed. The appearance of new,
additional resonances unneeded in the sole elastic channel is demonstrated.
