Ground States of the Nonlinear Schr{ö}dinger Equation on the Tadpole Graph with a Repulsive Delta Vertex Condition
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912372601389056 |
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| author | Duboscq, Romain Durand-Simonnet, Élio Coz, Stefan Le |
| author_facet | Duboscq, Romain Durand-Simonnet, Élio Coz, Stefan Le |
| contents | We consider the stationary nonlinear Schr{ö}dinger equation set on a tadpole graph with a repulsive delta vertex condition between the loop and the tail of the tadpole. We establish the existence of an action ground state when the size of the loop is either very small or very large. Our analysis relies on variational arguments, such as profile decomposition. When it exists, we study the shape of the ground state using ordinary differential equations arguments, such as the study of period functions. The theoretical results are completed with a numerical study. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04250 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ground States of the Nonlinear Schr{ö}dinger Equation on the Tadpole Graph with a Repulsive Delta Vertex Condition Duboscq, Romain Durand-Simonnet, Élio Coz, Stefan Le Analysis of PDEs We consider the stationary nonlinear Schr{ö}dinger equation set on a tadpole graph with a repulsive delta vertex condition between the loop and the tail of the tadpole. We establish the existence of an action ground state when the size of the loop is either very small or very large. Our analysis relies on variational arguments, such as profile decomposition. When it exists, we study the shape of the ground state using ordinary differential equations arguments, such as the study of period functions. The theoretical results are completed with a numerical study. |
| title | Ground States of the Nonlinear Schr{ö}dinger Equation on the Tadpole Graph with a Repulsive Delta Vertex Condition |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.04250 |