Exact analytic results are presented that give a general solution for
a pair of solitary waves which can propagate through a three- and a fi
ve-level system with their shapes invariant. These solitary waves vary
widely in shape and form: from ones for which the pulses have similar
shape to ones which have very different but ''complementary'' shapes.
A general type of solitary-wave pair which is insensitive to small pe
rturbations is identified.