Inverse scattering problem for the fifth-order Schr${\rm\bf\ddot{o}}$dinger operator on the whole axis

A method of solution for the inverse scattering problem for the linear fifth order Schr${\rm\ddot{o}}$dinger operator is found. Two closed systems of linear singular integral equations are obtained. From solutions to these equations, potential on the left and right half-axes is restored unambiguously.

Authors

Vladimir Alekseyevich Zolotarev (ORCID: https://orcid.org/0000-0002-2165-8552)

Publication Details

Journal: arXiv (Cornell University)
Published: 2026-10-29
DOI: https://doi.org/10.48550/arxiv.2610.39591
Primary Topic: Spectral Theory in Mathematical Physics
Type: preprint

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preprint

Inverse scattering problem for the fifth-order Schr${\rm\bf\ddot{o}}$dinger operator on the whole axis

Vladimir Alekseyevich Zolotarev

Oct 29, 2026

arXiv (Cornell University)

Spectral Theory in Mathematical Physics

preprint

Inverse scattering problem for the fifth-order Schr${\rm\bf\ddot{o}}$dinger operator on the whole axis

Vladimir Alekseyevich Zolotarev

October 29, 2026preprint en

Abstract

arXiv (Cornell University)

Spectral Theory in Mathematical Physics

DOI Open Access PDF OpenAlex

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Inverse scattering problem for the fifth-order Schr${\rm\bf\ddot{o}}$dinger operator on the whole axis — Vladimir Alekseyevich Zolotarev · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS