ИСТИНА

Generalized analytic functions naturally arise as solutions of the \bar\partial problem with extra reality constraints, for example, in the inverse problem for the Kadomtsev-Petviashvili 2 equation under assumption that the solutions are real. We show that the generalized analytic function equation admits Moutard transformations. If we consider the inverse scattering problem for the 2-dimensional Schrodinger operator at a fixed negative energy above the ground state, we have generalized analytic functions with special contour singularities. Recently we have shown that these singularities have the following characterization: can be locally removed by a Moutard transform. We also demonstrate, that the 2-dimensional conductivity equation admits Moutard transforms.