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Approximate direct and inverse scattering for the AKNS system.

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Title: Approximate direct and inverse scattering for the AKNS system.
Authors: Kravchenko, Vladislav V.1 (AUTHOR) vkravchenko@math.cinvestav.edu.mx
Source: Journal of Inverse & Ill-Posed Problems. Jun2026, Vol. 34 Issue 3, p395-418. 24p.
Subjects: Scattering (Mathematics), Inverse scattering transform, Power series, Numerical analysis, Integrable systems, Spectral theory, Linear systems
Abstract: We study the direct and inverse scattering problems for the Ablowitz–Kaup–Newell–Segur (AKNS) system. New representations for the Jost solutions are obtained in the form of the power series in terms of a transformed spectral parameter. In terms of that parameter, the Jost solutions are convergent power series in corresponding unit disks. For the coefficients of the series simple recurrent integration procedures are devised. Solution of the direct scattering problem reduces to computing the coefficients and locating zeros of corresponding analytic functions in the interior of the unit disk. Solution of the inverse scattering problem reduces to the solution of two systems of linear algebraic equations for the power series coefficients, while the potentials are recovered from the first coefficients. The overall approach leads to a simple and efficient method for the numerical solution of both direct and inverse scattering problems, which is illustrated by numerical examples. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Inverse & Ill-Posed Problems is the property of De Gruyter and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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PubTypeId: academicJournal
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  Data: Approximate direct and inverse scattering for the AKNS system.
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Inverse+%26+Ill-Posed+Problems%22">Journal of Inverse & Ill-Posed Problems</searchLink>. Jun2026, Vol. 34 Issue 3, p395-418. 24p.
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  Data: <searchLink fieldCode="DE" term="%22Scattering+%28Mathematics%29%22">Scattering (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Inverse+scattering+transform%22">Inverse scattering transform</searchLink><br /><searchLink fieldCode="DE" term="%22Power+series%22">Power series</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Integrable+systems%22">Integrable systems</searchLink><br /><searchLink fieldCode="DE" term="%22Spectral+theory%22">Spectral theory</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+systems%22">Linear systems</searchLink>
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  Data: We study the direct and inverse scattering problems for the Ablowitz–Kaup–Newell–Segur (AKNS) system. New representations for the Jost solutions are obtained in the form of the power series in terms of a transformed spectral parameter. In terms of that parameter, the Jost solutions are convergent power series in corresponding unit disks. For the coefficients of the series simple recurrent integration procedures are devised. Solution of the direct scattering problem reduces to computing the coefficients and locating zeros of corresponding analytic functions in the interior of the unit disk. Solution of the inverse scattering problem reduces to the solution of two systems of linear algebraic equations for the power series coefficients, while the potentials are recovered from the first coefficients. The overall approach leads to a simple and efficient method for the numerical solution of both direct and inverse scattering problems, which is illustrated by numerical examples. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Inverse & Ill-Posed Problems is the property of De Gruyter and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1515/jiip-2025-0096
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 24
        StartPage: 395
    Subjects:
      – SubjectFull: Scattering (Mathematics)
        Type: general
      – SubjectFull: Inverse scattering transform
        Type: general
      – SubjectFull: Power series
        Type: general
      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Integrable systems
        Type: general
      – SubjectFull: Spectral theory
        Type: general
      – SubjectFull: Linear systems
        Type: general
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      – TitleFull: Approximate direct and inverse scattering for the AKNS system.
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              M: 06
              Text: Jun2026
              Type: published
              Y: 2026
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              Value: 34
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            – TitleFull: Journal of Inverse & Ill-Posed Problems
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