Comment on:: "Reduction of static field equation of Faddeev model to first order PDE" [Phys. Lett. B 652 (2007) 384]

The authors of the article [M. Hirayama, C.-G. Shi, Phys. Lett. B 652 (2007) 384, arXiv: 0707.22071 propose an interesting method to solve the Faddeev model by reducing it to a set of first order PDEs. They first construct a vectorial quantity alpha, depending on the original field and its first derivatives, in terms of which the field equations reduce to a linear first order equation. Then they find vectors alpha(1) and alpha(2) which identically obey this linear first order equation. The last step consists in the identification of the alpha(i) with the original alpha as a function of the original field. Unfortunately, the authors overlook a constraint implied by their construction, which invalidates most of their subsequent results. (C) 2008 Elsevier B.V. All rights reserved.