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arXiv · 2509.06417

Inverse scattering problem for a cubic string having the shape of a step

Vladimir A. Zolotarev
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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 ``$+\infty$'', and its dual, correspondingly, of the waves from ``$-\infty$''. 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.

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Vladimir A. Zolotarev. 2025-09-08. Inverse scattering problem for a cubic string having the shape of a step. https://arxiv.org/abs/2509.06417

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