PT-symmetric branched optical lattices: Spectral properties and stability of solitons
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914236715761664 |
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| author | Tojakhmadova, O. K. Akhmadjanov, T. Akramov, M. E. |
| author_facet | Tojakhmadova, O. K. Akhmadjanov, T. Akramov, M. E. |
| contents | We investigate branched PT-symmetric optical lattices. We consider both the linear and nonlinear Schrödinger equations with a PT-symmetric periodic potential on the graph and solve them by imposing weighted vertex boundary conditions. A constraint derived from these vertex conditions determines the exceptional point of the system. In the PT unbroken phase, this constraint enforces PT-symmetric boundary conditions at the vertices, ensuring a purely real spectrum; its violation leads to the emergence of complex eigenvalues in the linear regime. In the nonlinear regime, the same constraint determines the linear stability of solitons: satisfying the constraint yields stable solitons, whereas violating it corresponds to unstable solitons. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03189 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | PT-symmetric branched optical lattices: Spectral properties and stability of solitons Tojakhmadova, O. K. Akhmadjanov, T. Akramov, M. E. Pattern Formation and Solitons Exactly Solvable and Integrable Systems We investigate branched PT-symmetric optical lattices. We consider both the linear and nonlinear Schrödinger equations with a PT-symmetric periodic potential on the graph and solve them by imposing weighted vertex boundary conditions. A constraint derived from these vertex conditions determines the exceptional point of the system. In the PT unbroken phase, this constraint enforces PT-symmetric boundary conditions at the vertices, ensuring a purely real spectrum; its violation leads to the emergence of complex eigenvalues in the linear regime. In the nonlinear regime, the same constraint determines the linear stability of solitons: satisfying the constraint yields stable solitons, whereas violating it corresponds to unstable solitons. |
| title | PT-symmetric branched optical lattices: Spectral properties and stability of solitons |
| topic | Pattern Formation and Solitons Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2601.03189 |