Moutard transform for the conductivity equation

2); (2) Lomonosov Moscow State University; (3) CMAP; 4) ((1) L.D. Landau Institute for Theoretical Physics; (4) Institute of Earthquake Prediction; Ecole polytechnique; France; P.G. Grinevich (1; RAS; R.G. Novikov (3

arxiv: 1801.00295 · v4 · pith:AUWEAL3Cnew · submitted 2017-12-31 · 🧮 math-ph · math.AP· math.MP· nlin.SI

Moutard transform for the conductivity equation

P.G. Grinevich (1 , 2) , R.G. Novikov (3 , 4) ((1) L.D. Landau Institute for Theoretical Physics , RAS , Russia , (2) Lomonosov Moscow State University , (3) CMAP

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Ecole polytechnique France (4) Institute of Earthquake Prediction Russia)

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classification 🧮 math-ph math.APmath.MPnlin.SI

keywords equationconductivitydarboux-moutardtransformstypeadditionadmitanalytic

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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.

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Moutard transform for the conductivity equation

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