Moutard transforms for the conductivity equation

  • P. G. GrinevichEmail author
  • R. G. Novikov


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 Schrödinger equation at zero energy are also shown.


Darboux–Moutard transforms Conductivity equation Integrability Generalized analytic functions 

Mathematics Subject Classification

35Q79 35Q60 35J15 35C05 30G20 



We thank Grégoire Allaire for drawing our attention to the articles [1, 21], which use a reduction in Eq. (47) to (49) via (48) and (50).


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.L.D. Landau Institute for Theoretical PhysicsChernogolovkaRussia
  2. 2.Faculty of Mechanics and MathematicsLomonosov Moscow State UniversityMoscowRussia
  3. 3.CNRS (UMR 7641), Centre de Mathématiques Appliquées, École PolytechniquePalaiseauFrance
  4. 4.IEPT RASMoscowRussia

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