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Spectral examination of a category of impulsive non-self-adjoint differential operator pencils featuring PT-symmetric potentials | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 12 آبان 1405 اصل مقاله (1.22 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.73121.3719 | ||
| نویسندگان | ||
| Rakib Efendiev1؛ Davron Aslonqulovich Juraev2؛ Alisher Orzu Rahimzoda3؛ Youssri Hassan Youssri4؛ Artion Kashuri* 5 | ||
| 1Department of Mathematics and Computer Science, Baku Engineering University, Baku AZ0102, Azerbaijan. | ||
| 21. Scientific Research Centre, Baku Engineering University, Baku AZ0102, Azerbaijan. 2. Scientific Laboratory of Dynamical Systems and Their Applications, Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent 100174, Uzbekistan. 3. Scientific Research Center, Institute of Military Aviation of the University of Military Security and Defense of the Republic of Uzbekistan, Karshi 180117, Uzbekistan. | ||
| 3Institute of Mathematics named after A. Juraev, National Academy of Sciences of Tajikistan, Dushanbe 734025, Tajikistan. | ||
| 4Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt. | ||
| 5Department of Mathematical Engineering, Polytechnic University of Tirana, 1001 Tirana, Albania. | ||
| چکیده | ||
| This paper investigates a class of impulsive non-self-adjoint differential operator pencils with complex periodic and PT-symmetric potentials defined on a semi-infinite domain. The study focuses on the spectral structure of the considered operators, including the characterization of eigenvalues, continuous spectrum, and spectral singularities arising from the interaction between non-Hermitian properties and impulsive conditions. Special solutions adapted to the discontinuous framework are constructed, and their analytical properties are examined to establish fundamental spectral results. A transfer matrix approach is developed to describe the influence of impulse conditions on the spectral behavior of the system. Furthermore, an inverse spectral problem is formulated and solved by reconstructing the potential functions from spectral data and reflection coefficients. The proposed reconstruction procedure provides a constructive and unique recovery of the operator parameters. The obtained results extend existing spectral theory for non-self-adjoint operators and contribute to the mathematical analysis of discontinuous media, wave propagation phenomena, and related inverse problems. | ||
| کلیدواژه‌ها | ||
| impulsive differential operators؛ non-self-adjoint operator pencils؛ PT-symmetric potentials؛ spectral analysis؛ jost solutions | ||
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آمار تعداد مشاهده مقاله: 3 تعداد دریافت فایل اصل مقاله: 4 |
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