English

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 (2+1)(2+1)-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