Uniqueness of the solution to the inverse problem of scattering theory for spectral parameter dependent Klein-Gordon s-wave equation
Yıl 2023,
, 59 - 70, 30.03.2023
Esra Kır Arpat
,
Turhan Köprübaşı
Öz
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.
Kaynakça
- 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
Yıl 2023,
, 59 - 70, 30.03.2023
Esra Kır Arpat
,
Turhan Köprübaşı
Kaynakça
- 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