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Year 2025, Volume: 8 Issue: 3, 112 - 120, 11.09.2025
https://doi.org/10.33187/jmsm.1629928

Abstract

References

  • [1] B. M. Levitan, I. S. Sargsjan, Sturm—Liouville and Dirac Operators, Springer Science+Business Media, Dordrecht, 1991.
  • [2] K. Aydemir, H. Olgar, O. S. Mukhtarov, et al., Differential operator equations with interface conditions in modified direct sum spaces, Filomat, 32(3) (2018), 921-931. https://doi.org/10.2298/FIL1803921A
  • [3] Y. Khalili, D. Baleanu, Recovering differential pencils with spectral boundary conditions and spectral jump conditions, J. Inequalities Appl., 2020 (2020), Article ID 262. https://doi.org/10.1186/s13660-020-02537-z
  • [4] O. S. Mukhtarov, M. Kadakal, F. S. Muhtarov, On discontinuous Sturm-Liouville problems with transmission conditions, J. Math. Kyoto Univ., 44(4) (2004), 779-798. https://doi.org/10.1215/kjm/1250281698
  • [5] E. Ugurlu, E. Bairamov, Spectral analysis of eigenparameter dependent boundary value transmission problems, J. Math. Anal. Appl., 413(1) (2014), 482-494. https://doi.org/10.1016/j.jmaa.2013.11.022
  • [6] A. M. Samoilenko, N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995.
  • [7] N. A. Perestyuk, Differential Equations with Impulse Effects: Multivalued Right-Hand Sides with Discontinuities, Walter de Gruyter, Berlin, 2011.
  • [8] V. Lakshmikantham, D. D. Bainov, P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, NJ USA, 1989.
  • [9] T. Koprubası, Y. Aygar, Discrete impulsive Sturm-Liouville equation with hyperbolic eigenparameter, Turk. J. Math., 46(2) (2022), 387-396. https://doi.org/10.3906/mat-2104-97
  • [10] Y. Aygar, T. Koprubası, A discrete boundary value problem with point interaction, Filomat, 36(18) (2022), 6279-6288. https://doi.org/10.2298/FIL2218279A
  • [11] S. Yardımcı, I. Erdal, Investigation of an impulsive Sturm-Liouville operator on semi axis, Hacet. J. Math. Stat., 48(5) (2019), 1409-1416.
  • [12] E. Bairamov, I. Erdal, S. Yardımcı, Spectral properties of an impulsive Sturm–Liouville operator, J. Inequalities Appl., (2018), Article ID 191, 16 pages. https://doi.org/10.1186/s13660-018-1781-0
  • [13] M. Bohner, S. Cebesoy, Spectral analysis of an impulsive quantum difference operator, Math. Methods Appl. Sci., 42(16) (2019), 5331-5339. https://doi.org/10.1002/mma.5348
  • [14] Y. Aygar, G. G. Ozbey, Scattering analysis of a quantum impulsive boundary value problem with spectral parameter, Hacet. J. Math. Stat., 51(1) (2022), 142-155. https://doi.org/10.15672/hujms.912015
  • [15] Y. Kucukevcilioglu, G. G. Ozbey, On the spectral and scattering properties of eigenparameter dependent discrete impulsive Sturm-Liouville equations, Turk. J. Math., 45(2) (2021), 988-1000. https://doi.org/10.3906/mat-2101-45
  • [16] B. P. Allahverdiev, H. Tuna, Resolvent operator of singular Dirac system with transmission conditions, Rad Hazu. Matematičke Znanosti, 23 (2019), 85-105. https://doi.org/10.21857/mnlqgc00ny
  • [17] E. Bairamov, S. Solmaz, 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
  • [18] E. Bairamov, S. Solmaz, Spectrum and scattering function of the impulsive discrete Dirac systems, Turk. J. Math., 42(6) (2018), 3182-3194. https://doi.org/10.3906/mat-1806-5
  • [19] E. Bairamov, S. Solmaz, S. Cebesoy, P, T, and PT-symmetries of impulsive Dirac systems, Hacet. J. Math. Stat., 49(4) (2020), 1234-1244. https: //doi.org/10.15672/hujms.542995
  • [20] S. Cebesoy, Examination of eigenvalues and spectral singularities of a discrete Dirac operator with an interaction point, Turk. J. Math., 46(1) (2022), 157-166. https://doi.org/10.3906/mat-2108-107
  • [21] H. M. Huseynov, An inverse scatterring problem for a system of Dirac equations with discontinuity conditions, Proc. Inst. Math. Mech., 40 (2014), 215-225.
  • [22] E. Ugurlu, Dirac systems with regular and singular transmission effects, Turk. J. Math., 41(1) (2017), 193-210. https://doi.org/10.3906/mat-1601-70
  • [23] E. Bairamov, O. A. Celebi, Spectrum and spectral expansion for the non-selfadjoint discrete Dirac operators, Q. J. Math., 50(200) (1999), 371-384. https://doi.org/10.1093/qjmath/50.200.371

Scattering Properties of Impulsive Discrete Dirac System with Hyperbolic Eigenparameter

Year 2025, Volume: 8 Issue: 3, 112 - 120, 11.09.2025
https://doi.org/10.33187/jmsm.1629928

Abstract

In this work, we examine the spectral and scattering properties of an impulsive discrete Dirac system with hyperbolic parameter such as resolvent operator, the set of eigenvalues, Jost function, scattering solutions and scattering function. The dependence of the boundary condition on the hyperbolic parameter changes the analyticity region of the Jost solution in the classical case. This provides a wide perspective on the applications of certain problems in physics, economics and engineering.

References

  • [1] B. M. Levitan, I. S. Sargsjan, Sturm—Liouville and Dirac Operators, Springer Science+Business Media, Dordrecht, 1991.
  • [2] K. Aydemir, H. Olgar, O. S. Mukhtarov, et al., Differential operator equations with interface conditions in modified direct sum spaces, Filomat, 32(3) (2018), 921-931. https://doi.org/10.2298/FIL1803921A
  • [3] Y. Khalili, D. Baleanu, Recovering differential pencils with spectral boundary conditions and spectral jump conditions, J. Inequalities Appl., 2020 (2020), Article ID 262. https://doi.org/10.1186/s13660-020-02537-z
  • [4] O. S. Mukhtarov, M. Kadakal, F. S. Muhtarov, On discontinuous Sturm-Liouville problems with transmission conditions, J. Math. Kyoto Univ., 44(4) (2004), 779-798. https://doi.org/10.1215/kjm/1250281698
  • [5] E. Ugurlu, E. Bairamov, Spectral analysis of eigenparameter dependent boundary value transmission problems, J. Math. Anal. Appl., 413(1) (2014), 482-494. https://doi.org/10.1016/j.jmaa.2013.11.022
  • [6] A. M. Samoilenko, N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995.
  • [7] N. A. Perestyuk, Differential Equations with Impulse Effects: Multivalued Right-Hand Sides with Discontinuities, Walter de Gruyter, Berlin, 2011.
  • [8] V. Lakshmikantham, D. D. Bainov, P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, NJ USA, 1989.
  • [9] T. Koprubası, Y. Aygar, Discrete impulsive Sturm-Liouville equation with hyperbolic eigenparameter, Turk. J. Math., 46(2) (2022), 387-396. https://doi.org/10.3906/mat-2104-97
  • [10] Y. Aygar, T. Koprubası, A discrete boundary value problem with point interaction, Filomat, 36(18) (2022), 6279-6288. https://doi.org/10.2298/FIL2218279A
  • [11] S. Yardımcı, I. Erdal, Investigation of an impulsive Sturm-Liouville operator on semi axis, Hacet. J. Math. Stat., 48(5) (2019), 1409-1416.
  • [12] E. Bairamov, I. Erdal, S. Yardımcı, Spectral properties of an impulsive Sturm–Liouville operator, J. Inequalities Appl., (2018), Article ID 191, 16 pages. https://doi.org/10.1186/s13660-018-1781-0
  • [13] M. Bohner, S. Cebesoy, Spectral analysis of an impulsive quantum difference operator, Math. Methods Appl. Sci., 42(16) (2019), 5331-5339. https://doi.org/10.1002/mma.5348
  • [14] Y. Aygar, G. G. Ozbey, Scattering analysis of a quantum impulsive boundary value problem with spectral parameter, Hacet. J. Math. Stat., 51(1) (2022), 142-155. https://doi.org/10.15672/hujms.912015
  • [15] Y. Kucukevcilioglu, G. G. Ozbey, On the spectral and scattering properties of eigenparameter dependent discrete impulsive Sturm-Liouville equations, Turk. J. Math., 45(2) (2021), 988-1000. https://doi.org/10.3906/mat-2101-45
  • [16] B. P. Allahverdiev, H. Tuna, Resolvent operator of singular Dirac system with transmission conditions, Rad Hazu. Matematičke Znanosti, 23 (2019), 85-105. https://doi.org/10.21857/mnlqgc00ny
  • [17] E. Bairamov, S. Solmaz, 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
  • [18] E. Bairamov, S. Solmaz, Spectrum and scattering function of the impulsive discrete Dirac systems, Turk. J. Math., 42(6) (2018), 3182-3194. https://doi.org/10.3906/mat-1806-5
  • [19] E. Bairamov, S. Solmaz, S. Cebesoy, P, T, and PT-symmetries of impulsive Dirac systems, Hacet. J. Math. Stat., 49(4) (2020), 1234-1244. https: //doi.org/10.15672/hujms.542995
  • [20] S. Cebesoy, Examination of eigenvalues and spectral singularities of a discrete Dirac operator with an interaction point, Turk. J. Math., 46(1) (2022), 157-166. https://doi.org/10.3906/mat-2108-107
  • [21] H. M. Huseynov, An inverse scatterring problem for a system of Dirac equations with discontinuity conditions, Proc. Inst. Math. Mech., 40 (2014), 215-225.
  • [22] E. Ugurlu, Dirac systems with regular and singular transmission effects, Turk. J. Math., 41(1) (2017), 193-210. https://doi.org/10.3906/mat-1601-70
  • [23] E. Bairamov, O. A. Celebi, Spectrum and spectral expansion for the non-selfadjoint discrete Dirac operators, Q. J. Math., 50(200) (1999), 371-384. https://doi.org/10.1093/qjmath/50.200.371
There are 23 citations in total.

Details

Primary Language English
Subjects Pure Mathematics (Other)
Journal Section Articles
Authors

Güler Başak Öznur 0000-0003-4130-5348

Early Pub Date August 18, 2025
Publication Date September 11, 2025
Submission Date January 30, 2025
Acceptance Date July 11, 2025
Published in Issue Year 2025 Volume: 8 Issue: 3

Cite

APA Öznur, G. B. (2025). Scattering Properties of Impulsive Discrete Dirac System with Hyperbolic Eigenparameter. Journal of Mathematical Sciences and Modelling, 8(3), 112-120. https://doi.org/10.33187/jmsm.1629928
AMA Öznur GB. Scattering Properties of Impulsive Discrete Dirac System with Hyperbolic Eigenparameter. Journal of Mathematical Sciences and Modelling. September 2025;8(3):112-120. doi:10.33187/jmsm.1629928
Chicago Öznur, Güler Başak. “Scattering Properties of Impulsive Discrete Dirac System With Hyperbolic Eigenparameter”. Journal of Mathematical Sciences and Modelling 8, no. 3 (September 2025): 112-20. https://doi.org/10.33187/jmsm.1629928.
EndNote Öznur GB (September 1, 2025) Scattering Properties of Impulsive Discrete Dirac System with Hyperbolic Eigenparameter. Journal of Mathematical Sciences and Modelling 8 3 112–120.
IEEE G. B. Öznur, “Scattering Properties of Impulsive Discrete Dirac System with Hyperbolic Eigenparameter”, Journal of Mathematical Sciences and Modelling, vol. 8, no. 3, pp. 112–120, 2025, doi: 10.33187/jmsm.1629928.
ISNAD Öznur, Güler Başak. “Scattering Properties of Impulsive Discrete Dirac System With Hyperbolic Eigenparameter”. Journal of Mathematical Sciences and Modelling 8/3 (September2025), 112-120. https://doi.org/10.33187/jmsm.1629928.
JAMA Öznur GB. Scattering Properties of Impulsive Discrete Dirac System with Hyperbolic Eigenparameter. Journal of Mathematical Sciences and Modelling. 2025;8:112–120.
MLA Öznur, Güler Başak. “Scattering Properties of Impulsive Discrete Dirac System With Hyperbolic Eigenparameter”. Journal of Mathematical Sciences and Modelling, vol. 8, no. 3, 2025, pp. 112-20, doi:10.33187/jmsm.1629928.
Vancouver Öznur GB. Scattering Properties of Impulsive Discrete Dirac System with Hyperbolic Eigenparameter. Journal of Mathematical Sciences and Modelling. 2025;8(3):112-20.

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