  We investigate the duality between minimal surfaces in Euclidean space and
maximal surfaces in Lorentz-Minkowski space in the family of rotational
surfaces. We study if the dual surfaces of two congruent rotational minimal (or
maximal) surfaces are congruent. We show that in the duality process by means
of a one-parameter group of rotations, it appears the family of Bonnet minimal
(maximal) surfaces and the Goursat transformations.
