Moutard transforms for the conductivity equation

Piotr G Grinevich (1) , Roman G Novikov (2)

1 L.D. Landau Institute for Theoretical Physics of RAS
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

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.

Mots clés: Darboux-Moutard transforms; Conductivity equation; Integrability; Inte-grability; Generalized analytic functions

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Piotr G Grinevich, Roman G Novikov. Moutard transforms for the conductivity equation. Letters in Mathematical Physics, 2019, 109 (10), pp.2209-2222. ⟨10.1007/s11005-019-01183-x⟩. ⟨hal-01673778v4⟩