Solving numerically the equations of motion for the effective Lagrangi
an describing supersymmetric QCD with the SU(2) gauge group, we find a
menagerie of complex domain wall solutions connecting different chira
lly asymmetric vacua. Some of these solutions are BPS-saturated walls;
they exist when the mass of the matter fields does not exceed some cr
itical value m < m() = 4.67059... There are also sphaleron branches (
saddle points of the energy functional). In the range m() < m < m(**)
approximate to 4.83, one of these branches becomes a local minimum (w
hich is not a BPS-saturated one). At m > m(*), the complex walls disa
ppear altogether and only the walls connecting a chirally asymmetric v
acuum with the chirally symmetric one survive. (C) 1998 Elsevier Scien
ce B.V.