Abstract
In this paper, the inverse spectral problem of the AKNS operator
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11971284
Funding source: Natural Science Foundation of Shaanxi Province
Award Identifier / Grant number: 2020JM-537
Funding statement: The research was supported by the National Natural Science Foundation of China (No. 11971284) and Natural Science Foundation of Shaanxi Province (No. 2020JM-537).
Acknowledgements
The authors would like to thank the referees of this paper for their helpful comments and suggestions.
References
[1] M. J. Ablowitz and A. S. Fokas, Complex Variables: Introduction and Applications, Cambridge Texts Appl. Math., Cambridge University, Cambridge, 2003. 10.1017/CBO9780511791246Suche in Google Scholar
[2] L. Amour, Inverse spectral theory for the AKNS system with separated boundary conditions, Inverse Problems 9 (1993), no. 5, 507–523. 10.1088/0266-5611/9/5/001Suche in Google Scholar
[3] G. Borg, Eine Umkehrung der Sturm–Liouvilleschen Eigenwertaufgabe. Bestimmung der Differentialgleichung durch die Eigenwerte, Acta Math. 78 (1946), 1–96. 10.1007/BF02421600Suche in Google Scholar
[4] S. Clark and F. Gesztesy, Weyl–Titchmarsh M-function asymptotics, local uniqueness results, trace formulas, and Borg-type theorems for Dirac operators, Trans. Amer. Math. Soc. 354 (2002), no. 9, 3475–3534. 10.1090/S0002-9947-02-03025-8Suche in Google Scholar
[5] A. A. Danielyan, B. M. Levitan and A. B. Khasanov, Asymptotics of the Weyl–Titchmarsh m-function in the case of the Dirac system, Mat. Zametki 50 (1991), no. 2, 67–76. 10.1007/BF01157568Suche in Google Scholar
[6] V. B. Daskalov and E. K. Khristov, Explicit formulae for the inverse problem for the regular Dirac operator, Inverse Problems 16 (2000), no. 1, 247–258. 10.1088/0266-5611/16/1/318Suche in Google Scholar
[7] R. del Rio and B. Grébert, Inverse spectral results for AKNS systems with partial information on the potentials, Math. Phys. Anal. Geom. 4 (2001), no. 3, 229–244. 10.1023/A:1012981630059Suche in Google Scholar
[8] G. Freiling and V. Yurko, Inverse Sturm–Liouville Problems and Their Applications, Nova Science, Huntington, 2001. Suche in Google Scholar
[9] M. G. Gasymov and T. T. Džabiev, Solution of the inverse problem by two spectra for the Dirac equation on a finite interval, Akad. Nauk Azerbaĭdžan. SSR Dokl. 22 (1966), no. 7, 3–6. Suche in Google Scholar
[10] B. Grébert and J.-C. Guillot, Gaps of one-dimensional periodic AKNS systems, Forum Math. 5 (1993), no. 5, 459–504. 10.1515/form.1993.5.459Suche in Google Scholar
[11] H. Hochstadt and B. Lieberman, An inverse Sturm–Liouville problem with mixed given data, SIAM J. Appl. Math. 34 (1978), no. 4, 676–680. 10.1137/0134054Suche in Google Scholar
[12] M. Horváth, On the inverse spectral theory of Schrödinger and Dirac operator, Trans. Amer. Math. Soc. 36 (2001), no. 10, 4155–4171. 10.1090/S0002-9947-01-02765-9Suche in Google Scholar
[13] B. J. Levin, Lectures on Entire Functions, Transl. Math. Monogr. 150, American Mathematical Society, Providence, 1996. 10.1090/mmono/150Suche in Google Scholar
[14] B. J. Levin and J. I. Ljubarskiĭ, Interpolation by entire functions belonging to special classes and related expansions in series of exponentials, Izv. Akad. Nauk SSSR Ser. Mat. 39 (1975), no. 3, 657–702. 10.1070/IM1975v009n03ABEH001493Suche in Google Scholar
[15] B. M. Levitan, Inverse Sturm–Liouville Problems, “Nauka”, Moscow, 1984. Suche in Google Scholar
[16] M. M. Malamud, Questions of uniqueness in inverse problems for systems of differential equations on a finite interval, Trans. Moscow Math. Soc. 60 (1999), 173–224. Suche in Google Scholar
[17] V. A. Marchenko, Sturm–Liouville Operators and Their Applications, Naukova Dumka, Kiev, 1977. Suche in Google Scholar
[18] Z. Wei, Z. Hu and Y. Xiang, Reconstruction of the solution of inverse Sturm–Liouville problem, Bound. Value Probl. 2024 (2024), Paper No. 55. 10.1186/s13661-024-01860-4Suche in Google Scholar
[19] Z. Wei and G. Wei, The uniqueness of inverse problem for the Dirac operators with partial information, Chinese Ann. Math. Ser. B 36 (2015), no. 2, 253–266. 10.1007/s11401-015-0885-9Suche in Google Scholar
[20] Z. Wei and G. Wei, Unique reconstruction of the potential for the interior transmission eigenvalue problem for spherically stratified media, Inverse Problems 36 (2020), no. 3, Article ID 035017. 10.1088/1361-6420/ab6e77Suche in Google Scholar
[21] Z. Wei and G. Wei, Mittag-Leffler expansions for inverse spectral problems with mixed data, Inverse Problems 39 (2023), no. 11, Article ID 115008. 10.1088/1361-6420/acfdc6Suche in Google Scholar
[22] C.-F. Yang and D.-Q. Liu, Half-inverse problem for the Dirac operator, Appl. Math. Lett. 87 (2019), 172–178. 10.1016/j.aml.2018.08.003Suche in Google Scholar
[23] R. M. Young, An Introduction to Nonharmonic Fourier Series, Pure Appl. Math. 93, Academic Press, New York, 1980. Suche in Google Scholar
© 2025 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- An inverse problem of finding a time-dependent parameter in a bilinear heat equation
- A novel method for computing core-EP inverse through elementary transformation
- Convergence rates for Tikhonov regularization of a coefficient identification problem
- Carleman estimate for stochastic degenerate wave equation with drift and its application
- Inverse initial problem under Nash strategy for stochastic reaction-diffusion equations with dynamic boundary conditions
- Understanding edge artifacts of the OSEM algorithm in emission tomography
- Unique reconstruction of the inverse spectral problem with mixed data for AKNS operator
- An inverse problem for nonlinear electrodynamic equations
Artikel in diesem Heft
- Frontmatter
- An inverse problem of finding a time-dependent parameter in a bilinear heat equation
- A novel method for computing core-EP inverse through elementary transformation
- Convergence rates for Tikhonov regularization of a coefficient identification problem
- Carleman estimate for stochastic degenerate wave equation with drift and its application
- Inverse initial problem under Nash strategy for stochastic reaction-diffusion equations with dynamic boundary conditions
- Understanding edge artifacts of the OSEM algorithm in emission tomography
- Unique reconstruction of the inverse spectral problem with mixed data for AKNS operator
- An inverse problem for nonlinear electrodynamic equations