Inverse scattering problem for a cubic string having the shape of a step
Classical Analysis and ODEs
2025-09-09 v1
Abstract
Problem for a cubic string having the shape of a step is studied. It is proved that here we have two scattering problems: the direct one and its dual. The direct problem describes scattering of the waves coming from ``'', and its dual, correspondingly, of the waves from ``''. The main systems of linear singular equations for both problems are obtained. It is shown how to unambiguously restore potential from the solutions to these equation systems.
Cite
@article{arxiv.2509.06417,
title = {Inverse scattering problem for a cubic string having the shape of a step},
author = {Vladimir A. Zolotarev},
journal= {arXiv preprint arXiv:2509.06417},
year = {2025}
}