  We show that Z(N) string's BPS equations are equivalent to the Hitchin's
equations (or self-duality equation) and also to the zero curvature condition.
We construct a general form for BPS Z(N) string solutions for arbitrary simple
gauge groups with non-trivial center. Depending on the vacuum solutions
considered, the Z(N) string's BPS equations reduce to different two dimensional
integrable field equations. For a particular vacuum we obtain the equation of
affine Toda field theory.
