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Uniqueness of the solution to the inverse problem of scattering theory for spectral parameter dependent Klein-Gordon s-wave equation

Year 2023, Volume: 72 Issue: 1, 59 - 70, 30.03.2023
https://doi.org/10.31801/cfsuasmas.1089508

Abstract

In the present work, the inverse problem of the scattering theory for Klein-Gordon s-wave equation with a spectral parameter in the boundary condition is investigated. We define the scattering data set, and obtain the main equation of operator. Furthermore, the uniqueness of the solution of the inverse problem is proved.

References

  • Aygar, Y., Bairamov, E., Scattering theory of impulsive Sturm-Liouville equation in quantum calculus, Bull. Malays. Math. Sci. Soc., 42(6) (2019), 3247-3259. https://doi.org/10.1007/s40840-018-0657-2
  • Aygar, Y., Bairamov, E., Ozbey, G. G., On the spectral and scattering properties of eigenparameter dependent discrete impulsive Sturm-Liouville equations, Turkish J. Math., 45(2) (2021), 988-1000. https://doi.org/10.3906/mat-2101-45
  • Bairamov, E., Aygar, Y., Cebesoy, S., Investigation of spectrum and scattering function of impulsive matrix difference operators, Filomat, 33(5) (2019), 1301-1312. https://doi.org/10.2298/FIL1905301B
  • Bairamov, E., Aygar, Y., Eren, B., Scattering theory of impulsive Sturm-Liouville equations, Filomat, 31(17) (2017), 5401-5409. https://doi.org/10.2298/FIL1717401B
  • Bairamov, E., Aygar, Y., Karslıoglu, D., Scattering analysis and spectrum of discrete Schrödinger equations with transmission conditions, Filomat, 31(17) (2017), 5391–5399. https://doi.org/10.2298/FIL1717391B
  • Bairamov, E., Aygar, Y., Oznur, G. B., Scattering properties of eigenparameter-dependent impulsive Sturm-Liouville equations, Bull. Malays. Math. Sci. Soc., 43(3) (2020), 2769-2781. https://doi.org/10.1007/s40840-019-00834-5
  • Bairamov, E., Celebi, A. O., Spectral properties of the Klein-Gordon s-wave equation with complex potential, Indian J. Pure Appl. Math., 28(6) (1997), 813-824.
  • Bairamov, E., Solmaz, S., Spectrum and scattering function of the impulsive discrete Dirac systems, Turkish J. Math., 42(6) (2018), 3182-3194. https://doi.org/10.3906/mat-1806-5
  • Bairamov, E., Solmaz, S., Scattering theory of Dirac operator with the impulsive condition on whole axis, Math. Methods Appl. Sci., 44(9) (2021), 7732-7746. https://doi.org/10.1002/mma.6645
  • Jaulent, M., Jean, C., The inverse s-wave scattering problem for a class of potentials depending on energy, Comm. Math. Phys., 28 (1972), 177-220. https://doi.org/10.1007/BF01645775
  • Maksudov, F. G., Bairamov, E., Orujeva, R. U., An inverse scattering problem for an infinite Jacobi matrix with operator elements (Russian), Dokl. Akad. Nauk., 323 (3) (1992), 415-419.
  • Mamedov, Kh. R., Uniqueness of the solution to the inverse problem of scattering theory for the Sturm-Liouville operator with a spectral parameter in the boundary condition, Mathematical Notes, 74(1) (2003), 136-140. https://doi.org/10.4213/mzm587
  • Marchenko, V. A., Sturm-Liouville Operators and Applications, Birkhauser Verlag, Basel, 1986. https://doi.org/10.1007/978-3-0348-5485-6
  • Tunca, G. B., Spectral properties of the Klein-Gordon s-wave equation with spectral parameter-dependent boundary condition, Int. J. Math. Math. Sci., 27 (2004), 1437-1445. https://doi.org/10.1155/S0161171204203088
  • Tunca, G. B., Arpat, E. K., Uniqueness of the solution to the inverse problem of scattering theory for the Sturm-Liouville operator system with a spectral parameter in the boundary condition, Gazi Univ. J. Sci., 29(1) (2016), 135-142. https://doi.org/10.1155/S0161171204203088
Year 2023, Volume: 72 Issue: 1, 59 - 70, 30.03.2023
https://doi.org/10.31801/cfsuasmas.1089508

Abstract

References

  • Aygar, Y., Bairamov, E., Scattering theory of impulsive Sturm-Liouville equation in quantum calculus, Bull. Malays. Math. Sci. Soc., 42(6) (2019), 3247-3259. https://doi.org/10.1007/s40840-018-0657-2
  • Aygar, Y., Bairamov, E., Ozbey, G. G., On the spectral and scattering properties of eigenparameter dependent discrete impulsive Sturm-Liouville equations, Turkish J. Math., 45(2) (2021), 988-1000. https://doi.org/10.3906/mat-2101-45
  • Bairamov, E., Aygar, Y., Cebesoy, S., Investigation of spectrum and scattering function of impulsive matrix difference operators, Filomat, 33(5) (2019), 1301-1312. https://doi.org/10.2298/FIL1905301B
  • Bairamov, E., Aygar, Y., Eren, B., Scattering theory of impulsive Sturm-Liouville equations, Filomat, 31(17) (2017), 5401-5409. https://doi.org/10.2298/FIL1717401B
  • Bairamov, E., Aygar, Y., Karslıoglu, D., Scattering analysis and spectrum of discrete Schrödinger equations with transmission conditions, Filomat, 31(17) (2017), 5391–5399. https://doi.org/10.2298/FIL1717391B
  • Bairamov, E., Aygar, Y., Oznur, G. B., Scattering properties of eigenparameter-dependent impulsive Sturm-Liouville equations, Bull. Malays. Math. Sci. Soc., 43(3) (2020), 2769-2781. https://doi.org/10.1007/s40840-019-00834-5
  • Bairamov, E., Celebi, A. O., Spectral properties of the Klein-Gordon s-wave equation with complex potential, Indian J. Pure Appl. Math., 28(6) (1997), 813-824.
  • Bairamov, E., Solmaz, S., Spectrum and scattering function of the impulsive discrete Dirac systems, Turkish J. Math., 42(6) (2018), 3182-3194. https://doi.org/10.3906/mat-1806-5
  • Bairamov, E., Solmaz, S., Scattering theory of Dirac operator with the impulsive condition on whole axis, Math. Methods Appl. Sci., 44(9) (2021), 7732-7746. https://doi.org/10.1002/mma.6645
  • Jaulent, M., Jean, C., The inverse s-wave scattering problem for a class of potentials depending on energy, Comm. Math. Phys., 28 (1972), 177-220. https://doi.org/10.1007/BF01645775
  • Maksudov, F. G., Bairamov, E., Orujeva, R. U., An inverse scattering problem for an infinite Jacobi matrix with operator elements (Russian), Dokl. Akad. Nauk., 323 (3) (1992), 415-419.
  • Mamedov, Kh. R., Uniqueness of the solution to the inverse problem of scattering theory for the Sturm-Liouville operator with a spectral parameter in the boundary condition, Mathematical Notes, 74(1) (2003), 136-140. https://doi.org/10.4213/mzm587
  • Marchenko, V. A., Sturm-Liouville Operators and Applications, Birkhauser Verlag, Basel, 1986. https://doi.org/10.1007/978-3-0348-5485-6
  • Tunca, G. B., Spectral properties of the Klein-Gordon s-wave equation with spectral parameter-dependent boundary condition, Int. J. Math. Math. Sci., 27 (2004), 1437-1445. https://doi.org/10.1155/S0161171204203088
  • Tunca, G. B., Arpat, E. K., Uniqueness of the solution to the inverse problem of scattering theory for the Sturm-Liouville operator system with a spectral parameter in the boundary condition, Gazi Univ. J. Sci., 29(1) (2016), 135-142. https://doi.org/10.1155/S0161171204203088
There are 15 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Esra Kır Arpat 0000-0002-6322-5130

Turhan Köprübaşı 0000-0003-1551-1527

Publication Date March 30, 2023
Submission Date March 17, 2022
Acceptance Date July 28, 2022
Published in Issue Year 2023 Volume: 72 Issue: 1

Cite

APA Kır Arpat, E., & Köprübaşı, T. (2023). Uniqueness of the solution to the inverse problem of scattering theory for spectral parameter dependent Klein-Gordon s-wave equation. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 72(1), 59-70. https://doi.org/10.31801/cfsuasmas.1089508
AMA Kır Arpat E, Köprübaşı T. Uniqueness of the solution to the inverse problem of scattering theory for spectral parameter dependent Klein-Gordon s-wave equation. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. March 2023;72(1):59-70. doi:10.31801/cfsuasmas.1089508
Chicago Kır Arpat, Esra, and Turhan Köprübaşı. “Uniqueness of the Solution to the Inverse Problem of Scattering Theory for Spectral Parameter Dependent Klein-Gordon S-Wave Equation”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72, no. 1 (March 2023): 59-70. https://doi.org/10.31801/cfsuasmas.1089508.
EndNote Kır Arpat E, Köprübaşı T (March 1, 2023) Uniqueness of the solution to the inverse problem of scattering theory for spectral parameter dependent Klein-Gordon s-wave equation. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72 1 59–70.
IEEE E. Kır Arpat and T. Köprübaşı, “Uniqueness of the solution to the inverse problem of scattering theory for spectral parameter dependent Klein-Gordon s-wave equation”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 72, no. 1, pp. 59–70, 2023, doi: 10.31801/cfsuasmas.1089508.
ISNAD Kır Arpat, Esra - Köprübaşı, Turhan. “Uniqueness of the Solution to the Inverse Problem of Scattering Theory for Spectral Parameter Dependent Klein-Gordon S-Wave Equation”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72/1 (March 2023), 59-70. https://doi.org/10.31801/cfsuasmas.1089508.
JAMA Kır Arpat E, Köprübaşı T. Uniqueness of the solution to the inverse problem of scattering theory for spectral parameter dependent Klein-Gordon s-wave equation. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72:59–70.
MLA Kır Arpat, Esra and Turhan Köprübaşı. “Uniqueness of the Solution to the Inverse Problem of Scattering Theory for Spectral Parameter Dependent Klein-Gordon S-Wave Equation”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 72, no. 1, 2023, pp. 59-70, doi:10.31801/cfsuasmas.1089508.
Vancouver Kır Arpat E, Köprübaşı T. Uniqueness of the solution to the inverse problem of scattering theory for spectral parameter dependent Klein-Gordon s-wave equation. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72(1):59-70.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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