Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2009-05-05
Inverse Problems 25 (2009) 105003
Nonlinear Sciences
Exactly Solvable and Integrable Systems
final version that will appear in Inverse Problems
Scientific paper
10.1088/0266-5611/25/10/105003
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 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 wave function change when a discrete eigenvalue is added to the spectrum.
Aktosun Tuncay
der Mee Cornelis van
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