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

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
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
preprint en

Abstract

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.

arXiv (Cornell University)
Spectral Theory in Mathematical Physics
DOIOpen Access PDFOpenAlex
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