Ambiguities and almost reflectionless potentials

摘要

This paper considers possible ambiguities associated with perturbations on reflectionless solutions of the Gel'Fand-Levitan Equation. By considering perturbations on the spectral measure function and the potential it is shown that no ambiguity exists with respect to spectral measure perturbations. However, it is shown that first-order effects in the potential can lead to second-order effects in the spectral measure function, thereby demonstrating an ambiguity with respect to first-order approximations.