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,, Russia, (3) CMAP, Ecole Polytechnique, France, (4) Institute of Earthquake, Prediction, Russia)
TL;DR
This paper develops Darboux-Moutard transforms for the 2D conductivity equation, extending previous work on generalized analytic functions and exploring connections to multidimensional cases and the Schrödinger equation at zero energy.
Contribution
It introduces Darboux-Moutard transforms for the conductivity equation and demonstrates their potential extension to higher dimensions and links to Schrödinger equations.
Findings
Constructed Darboux-Moutard transforms for 2D conductivity equation
Extended transforms to multidimensional conductivity equations
Established relations to zero-energy Schrödinger equation
Abstract
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNumerical methods in inverse problems · Nonlinear Waves and Solitons · Differential Equations and Boundary Problems