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Moutard transform approach to generalized analytic functions with contour poles. (English) Zbl 1351.30034

The authors study the equation of generalized analytic functions \[ \partial_{\overline{z}}\psi =u\overline{\psi} \] and the conjugate equation \[ \partial_{\overline{z}}\psi^{+} = -\overline{u}\overline{\psi}^{+} \] for coefficient \(u\) with contour poles. They obtain composition and inversion formulas for the simple Moutard-type transforms for these equations, and show that the equation of meromorphic class with a simple contour pole is reducible to a regular one via an appropriate Moutard-type transform.

MSC:

30G20 Generalizations of Bers and Vekua type (pseudoanalytic, \(p\)-analytic, etc.)
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
35J46 First-order elliptic systems
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