  We construct exact solutions of BPS pion domain walls in the four-dimensional
$\mathcal{N}=1$ supersymmetric SU(N) chiral Lagrangian with pion masses
introduced via linear and quadratic superpotentials. The model admits N
discrete vacua in the center of SU(N) for the linear superpotential. In
addition to the latter, new vacua appear for the quadratic superpotential. We
find that the domain wall solutions of pions (Nambu-Goldstone bosons) that
interpolate between a pair of (pion) vacua preserve half of supersymmetry.
Contrary to our expectations, we have not been able to find domain walls
involving the quasi-Nambu-Goldstone bosons present in the theory, which in turn
has the consequence that not all vacua of the theory are connected by a BPS
domain wall solution.
