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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.21200 |
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| _version_ | 1866908435847577600 |
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| author | Pava, Jaime Angulo Yépez, Andrés Gerardo Pérez |
| author_facet | Pava, Jaime Angulo Yépez, Andrés Gerardo Pérez |
| contents | This work aims to study some dynamical aspects of the nonlinear logarithmic Schrödinger equation (NLS-log) on a tadpole graph, namely, a graph consisting of a circle with a half-line attached at a single vertex. By considering Neumann-Kirchhoff boundary conditions at the junction we show the existence and the orbital stability of standing wave solutions with a profile determined by a positive single-lobe state. Via a splitting-eigenvalue method, we identify the Morse index and the nullity index of a specific linearized operator around a positive singlelobe state. To our knowledge, the results contained in this paper are the first to study the (NLS-log) on tadpole graphs. In particular, our approach has the prospect of being extended to study stability properties of other bound states for the (NLS-log) on a tadpole graph or other non-compact metric graph such as a looping-edge graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_21200 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence and orbital stability of standing-wave solutions of the NLS-log equation on a tadpole graph Pava, Jaime Angulo Yépez, Andrés Gerardo Pérez Analysis of PDEs This work aims to study some dynamical aspects of the nonlinear logarithmic Schrödinger equation (NLS-log) on a tadpole graph, namely, a graph consisting of a circle with a half-line attached at a single vertex. By considering Neumann-Kirchhoff boundary conditions at the junction we show the existence and the orbital stability of standing wave solutions with a profile determined by a positive single-lobe state. Via a splitting-eigenvalue method, we identify the Morse index and the nullity index of a specific linearized operator around a positive singlelobe state. To our knowledge, the results contained in this paper are the first to study the (NLS-log) on tadpole graphs. In particular, our approach has the prospect of being extended to study stability properties of other bound states for the (NLS-log) on a tadpole graph or other non-compact metric graph such as a looping-edge graphs. |
| title | Existence and orbital stability of standing-wave solutions of the NLS-log equation on a tadpole graph |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2502.21200 |