Research Article

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

Volume: 72 Number: 1 March 30, 2023
EN

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

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.

Keywords

References

  1. 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
  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
  3. 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
  4. 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
  5. 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
  6. 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
  7. 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.
  8. 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

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

March 30, 2023

Submission Date

March 17, 2022

Acceptance Date

July 28, 2022

Published in Issue

Year 1970 Volume: 72 Number: 1

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
1.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. doi:10.31801/cfsuasmas.1089508
Chicago
Kır Arpat, Esra, and Turhan Köprübaşı. 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.
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
[1]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, Mar. 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 1, 2023): 59-70. https://doi.org/10.31801/cfsuasmas.1089508.
JAMA
1.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, Mar. 2023, pp. 59-70, doi:10.31801/cfsuasmas.1089508.
Vancouver
1.Esra Kır Arpat, Turhan 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. 2023 Mar. 1;72(1):59-70. doi:10.31801/cfsuasmas.1089508

Cited By

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

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