Darboux transformation of boundary conditions of regular Dirac Sturm--Liouville problem

TL;DR

This paper demonstrates that applying Darboux transformations to boundary conditions in Dirac Sturm--Liouville problems results in zero-valued boundary conditions, regardless of the initial conditions.

Contribution

It reveals a universal property of boundary conditions after Darboux transformation in Dirac Sturm--Liouville problems.

Findings

Boundary conditions become zero-valued after Darboux transformation.

This property holds regardless of initial boundary conditions.

The result simplifies analysis of transformed problems.

Abstract

It is shown that boundary conditions of the Darboux transformed Dirac Sturm--Liouville problem are always zero-valued independently on boundary conditions of initial problem.