Creation and annihilation of point-potentials using Moutard-type transform in spectral variable

TL;DR

This paper extends a Moutard-type transform method to create and annihilate point potentials in the spectral data of the 2D Schrödinger equation, demonstrating its effectiveness for point potentials.

Contribution

It develops a novel approach using Moutard-type transforms to manipulate point potentials within the spectral data framework.

Findings

Successfully applies the method to point potentials

Demonstrates creation and annihilation of contour singularities

Extends previous methods to a new class of potentials

Abstract

We continue to develop the method for creation and annihilation of contour singularities in the $\bar\partial$--spectral data for the two-dimensional Schr\"odinger equation at fixed energy. Our method is based on the Moutard-type transforms for generalized analytic functions. In this note we show that this approach successfully works for point potentials.