  In this paper we study certain aspects of the complete integrability of the
Generalized Weierstrass system in the context of the Sinh-Gordon type equation.
Using the conditional symmetry approach, we construct the B\"{a}cklund
transformation for the Generalized Weierstrass system which is determined by
coupled Riccati equations. Next a linear spectral problem is found which is
determined by nonsingular $2 \times 2$ matrices based on an $sl (2, \mathbb C)$
representation. We derive the explicit form of the Darboux transformation for
the Weierstrass system. New classes of multisoliton solutions of the
Generalized Weierstrass system are obtained through the use of the B\"{a}cklund
transformation and some physical applications of these results in the area of
classical string theory are presented.
