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arXiv · 0906.5141

The Moutard transformation: an algebraic formalism via pseudodifferential operators and applications

I. A. Taimanov·S. P. Tsarev
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Abstract

We consider the Moutard transformation which is a two-dimensional 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 Schroedinger operators. An application to some problems of the spectral theory of two-dimensional Schroedinger operators and to the $(2+1)$-dimensional Novikov--Veselov equation is sketched.

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I. A. Taimanov, S. P. Tsarev. 2009-06-28. The Moutard transformation: an algebraic formalism via pseudodifferential operators and applications. https://arxiv.org/abs/0906.5141

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