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Explicit solutions in inverse scattering method for negative-order AKNS equations.

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Title: Explicit solutions in inverse scattering method for negative-order AKNS equations.
Authors: Sabaz, Cihan1 (AUTHOR) cihansabaz@gmail.com, Ismailov, Mansur I. (AUTHOR) mismailov@gtu.edu.tr
Source: Reports on Mathematical Physics. Apr2026, Vol. 97 Issue 2, p257-273. 17p.
Subjects: Inverse scattering transform, Lax pair, Integrable systems, Solitons
Abstract: In this paper, the Lax pairs of the negative-order AKNS equations are presented. The explicit solutions (classical N -soliton and singular kink wave solutions) are derived using the inverse scattering method. The auxiliary spectral problem is formulated as the classical Zakharov-Shabat system with real symmetric and real anti-symmetric potentials. By recalling results from the inverse scattering problem and utilizing the time evolution of the scattering data, explicit solutions for the negative-order AKNS equations corresponding to symmetric and anti-symmetric potentials are obtained through the Gelfand-Levitan-Marchenko equation. [ABSTRACT FROM AUTHOR]
Copyright of Reports on Mathematical Physics is the property of Pergamon Press - An Imprint of Elsevier Science 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.)
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An: 193806838
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  Data: Explicit solutions in inverse scattering method for negative-order AKNS equations.
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  Data: <searchLink fieldCode="AR" term="%22Sabaz%2C+Cihan%22">Sabaz, Cihan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> cihansabaz@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Ismailov%2C+Mansur+I%2E%22">Ismailov, Mansur I.</searchLink> (AUTHOR)<i> mismailov@gtu.edu.tr</i>
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  Data: <searchLink fieldCode="JN" term="%22Reports+on+Mathematical+Physics%22">Reports on Mathematical Physics</searchLink>. Apr2026, Vol. 97 Issue 2, p257-273. 17p.
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  Data: <searchLink fieldCode="DE" term="%22Inverse+scattering+transform%22">Inverse scattering transform</searchLink><br /><searchLink fieldCode="DE" term="%22Lax+pair%22">Lax pair</searchLink><br /><searchLink fieldCode="DE" term="%22Integrable+systems%22">Integrable systems</searchLink><br /><searchLink fieldCode="DE" term="%22Solitons%22">Solitons</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: In this paper, the Lax pairs of the negative-order AKNS equations are presented. The explicit solutions (classical N -soliton and singular kink wave solutions) are derived using the inverse scattering method. The auxiliary spectral problem is formulated as the classical Zakharov-Shabat system with real symmetric and real anti-symmetric potentials. By recalling results from the inverse scattering problem and utilizing the time evolution of the scattering data, explicit solutions for the negative-order AKNS equations corresponding to symmetric and anti-symmetric potentials are obtained through the Gelfand-Levitan-Marchenko equation. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Reports on Mathematical Physics is the property of Pergamon Press - An Imprint of Elsevier Science 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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    Identifiers:
      – Type: doi
        Value: 10.1016/S0034-4877(26)00027-3
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      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 17
        StartPage: 257
    Subjects:
      – SubjectFull: Inverse scattering transform
        Type: general
      – SubjectFull: Lax pair
        Type: general
      – SubjectFull: Integrable systems
        Type: general
      – SubjectFull: Solitons
        Type: general
    Titles:
      – TitleFull: Explicit solutions in inverse scattering method for negative-order AKNS equations.
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          Name:
            NameFull: Sabaz, Cihan
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            NameFull: Ismailov, Mansur I.
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          Dates:
            – D: 01
              M: 04
              Text: Apr2026
              Type: published
              Y: 2026
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              Value: 97
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              Value: 2
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            – TitleFull: Reports on Mathematical Physics
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