The Moutard Transformation: an Algebraic Formalism via Pseudodifferential Operators and Applications
نویسندگان
چکیده
In this paper we consider the Moutard transformation [9] which is a twodimensional version of the well-known Darboux transformation. We give an algebraic interpretation of the Moutard transformation as a conjugation in an appropriate ring and the corresponding version of the algebro-geometric formalism for two-dimensional Schrödinger operators. An application to some problems of the spectral theory of twodimensional Schrödinger operators and to the (2 + 1)-dimensional Novikov–Veselov equation is sketched.
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