  We consider an exact solvable interacting spinful Kitaev chain which is a
generalization of the Mattis-Nam model. A nearest-neighbor dimerized
interaction favoring the production of disjoint molecules drives the quantum
phase into an insulating one. The phases are characterized statically and
dynamically in terms of magnetization and spin-singlet correlations by using
the exact solution. The model is shown to be exactly solvable also in the
presence of boundary interactions which are originated from a spin-singlet
superconducting pairing and a magnetic field. We exploit the exact solution to
investigate the out-of-equilibrium dynamics as due to a quench at the boundary.
The propagation of the disturbance in nearest-neighbor magnetic and
spin-singlet pairing displays a ballistic behavior for long times with
different velocities.
