The Journal of Geometric Analysis

, Volume 26, Issue 4, pp 2984–2995 | Cite as

Moutard Transform for Generalized Analytic Functions

  • P. G. Grinevich
  • R. G. NovikovEmail author


We construct a Moutard-type transform for generalized analytic functions. The first theorems and the first explicit examples in this connection are given.


Generalized analytic functions Integrability Moutard transform 

Mathematics Subject Classification

30G20 37K35 35J46 



The main part of the work was fulfilled during the visit of the first author to the Centre de Mathématiques Appliquées of École Polytechnique in October 2015. The first author was partially supported by the Russian Foundation for Basic Research, Grant 13-01-12469 ofi-m2, by the Program “Leading scientific schools” (Grant NSh-4833.2014.1), by the Program “Fundamental problems of nonlinear dynamics”.


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Copyright information

© Mathematica Josephina, Inc. 2015

Authors and Affiliations

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

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