The Moutard transformation and two-dimensional multi-point delta-type potentials

TL;DR

This paper applies the Moutard transformation to construct two-dimensional multi-point delta potentials for Schrödinger operators, revealing their reflectionless nature and isospectral deformations at zero energy.

Contribution

It introduces a novel method for generating multi-point delta potentials in 2D Schrödinger operators using the Moutard transformation, highlighting their reflectionless properties.

Findings

Constructed explicit multi-point delta potentials

Demonstrated reflectionless scattering data

Identified isospectral deformations at zero energy

Abstract

In the framework of the Moutard transformation formalism we find multi-point delta-type potentials of two-dimensional Schrodinger operators and their isospectral deformations on the zero energy level. In particular, these potentials are "reflectionless" in the sense of the Faddeev generalized "scattering" data.