Year: 2009
Type: article
Abstract: We analyze a certain class of integral equations related to Marchenko equations and Gel'fand–Levitan equations associated with various systems of ordinary differential operators. When the integral operator is perturbed by a finite-rank perturbation, we explicitly evaluate the change in the solution. We show how this result provides a unified approach to derive Darboux transformations associated with various systems of ordinary differential operators. We illustrate our theory by deriving the Darboux transformation for the Zakharov–Shabat system and show how the potential and wavefunction change when a discrete eigenvalue is added to the spectrum.
Source: Inverse Problems
Authors: Tuncay Aktosun, Cornelis van der Mee
Institutions: The University of Texas at Arlington, University of Cagliari
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2029450669