English

Moutard transform for the conductivity equation

Mathematical Physics 2019-03-05 v4 Analysis of PDEs math.MP Exactly Solvable and Integrable Systems

Abstract

We construct Darboux-Moutard type transforms for the two-dimensional conductivity equation. This result continues our recent studies of Darboux-Moutard type transforms for generalized analytic functions. In addition, at least, some of the Darboux-Moutard type transforms of the present work admit direct extension to the conductivity equation in multidimensions. Relations to the Schr\"odinger equation at zero energy are also shown.

Keywords

Cite

@article{arxiv.1801.00295,
  title  = {Moutard transform for the conductivity equation},
  author = {P. G. Grinevich and R. G. Novikov},
  journal= {arXiv preprint arXiv:1801.00295},
  year   = {2019}
}

Comments

LaTeX, 17 pages, some additional materials and references were added

R2 v1 2026-06-22T23:33:19.681Z