  Transformations between different analytic descriptions of constant mean
curvature (CMC) surfaces are established. In particular, it is demonstrated
that the system \[ \begin{split} &\partial \psi_{1} = (|\psi_{1}|^{2} +
|\psi_{2}|^{2}) \psi_{2} \\ &\bar{\partial} \psi_{2} =- (|\psi_{1}|^{2} +
|\psi_{2}|^{2}) \psi_{1} \end{split} \] descriptive of CMC surfaces within the
framework of the generalized Weierstrass representation, decouples into a
direct sum of the elliptic Sh-Gordon and Laplace equations. Connections of this
system with the sigma model equations are established. It is pointed out, that
the instanton solutions correspond to different Weierstrass parametrizations of
the standard sphere $S^{2} \subset E^{3}$.
