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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. 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