The Moutard transformation of two-dimensional Dirac operators and   conformal geometry of surfaces in the four-space
  The Moutard transformation for a two-dimensional Dirac operator with a complex-valued potential is constructed. It is showed that this transformation relates the potentials of Weierstrass representations of surfaces related by a composition of the inversion and a reflection with respect to an axis. It is given an analytical description of an explicit example of such a transformation which results in a creation of double points on the spectral curve of a Dirac operator with a double-periodic potential. 
R.M. Matuev, I.A. Taimanov
nlin.SI math.DG