Moutard transforms for the conductivity equation

Moutard transforms for the conductivity equation

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 dir...

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Veröffentlicht in:Letters in mathematical physics 2019-10, Vol.109 (10), p.2209-2222
Hauptverfasser: Grinevich, P. G., Novikov, R. G.
Format: Artikel
Sprache:eng
Schlagworte:
Analysis of PDEs
Analytic functions
Complex Systems
Conductivity
Geometry
Group Theory and Generalizations
Mathematical and Computational Physics
Mathematical Physics
Mathematics
Physics
Physics and Astronomy
Schrodinger equation
Theoretical
Transformations (mathematics)
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Zusammenfassung: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.
ISSN:0377-9017
1573-0530
DOI:10.1007/s11005-019-01183-x