  We explore dynamics of discrete breathers and multi-breathers in finite
one-dimensional chain. The model involves parabolic on-site potential with
rigid constraints and linear nearest-neighbor coupling. The rigid non-ideal
impact constraints are the only source of nonlinearity and damping in the
model. The model allows derivation of exact analytic solutions for the
breathers and multi-breathers with arbitrary set of localization sites, both in
conservative and forced-damped settings. We choose periodic boundary
conditions; exact solutions for other types of the boundary conditions are also
possible. Local character of the nonlinearity allows explicit derivation of a
monodromy matrix for the breather solutions. Consequently, a stability of the
derived breather and multi-breather solutions can be efficiently studied in the
framework of simple methods of linear algebra, and with rather moderate
computational efforts. We demonstrate that finitness of the chain fragment and
proximity of the localization sites strongly effect existence and stability
patterns of these localized solutions.
