The Moutard transformation: an algebraic formalism via pseudodifferential operators and applications
Mathematical Physics
2010-08-13 v1 math.MP
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 -dimensional Novikov--Veselov equation is sketched.
Keywords
Cite
@article{arxiv.0906.5141,
title = {The Moutard transformation: an algebraic formalism via pseudodifferential operators and applications},
author = {I. A. Taimanov and S. P. Tsarev},
journal= {arXiv preprint arXiv:0906.5141},
year = {2010}
}
Comments
15 pages, 2 figures