Stability transitions of NLS action ground-states on metric graphs
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912456139341824 |
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| author | Agostinho, Francisco Correia, Simão Tavares, Hugo |
| author_facet | Agostinho, Francisco Correia, Simão Tavares, Hugo |
| contents | We study the orbital stability of action ground-states of the nonlinear Schrödinger equation over two particular cases of metric graphs, the $\mathcal{T}$ and the tadpole graphs. We show the existence of stability transitions near the $L^2$-critical exponent, a new dynamical feature of the nonlinear Schrödinger equation. More precisely, as the frequency $λ$ increases, the action ground-state transitions from stable to unstable and then back to stable (or vice-versa).
This result is complemented with the stability analysis of ground-states in the asymptotic cases of low/high frequency and weak/strong nonlinear interaction. Finally, we present a numerical simulation of the stability of action ground-states depending on the nonlinearity and the frequency parameter, which validates the aforementioned theoretical results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_23166 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability transitions of NLS action ground-states on metric graphs Agostinho, Francisco Correia, Simão Tavares, Hugo Analysis of PDEs Mathematical Physics Classical Analysis and ODEs 34C37, 35B35, 35Q55, 35R02, {37K45}, 70K05 We study the orbital stability of action ground-states of the nonlinear Schrödinger equation over two particular cases of metric graphs, the $\mathcal{T}$ and the tadpole graphs. We show the existence of stability transitions near the $L^2$-critical exponent, a new dynamical feature of the nonlinear Schrödinger equation. More precisely, as the frequency $λ$ increases, the action ground-state transitions from stable to unstable and then back to stable (or vice-versa). This result is complemented with the stability analysis of ground-states in the asymptotic cases of low/high frequency and weak/strong nonlinear interaction. Finally, we present a numerical simulation of the stability of action ground-states depending on the nonlinearity and the frequency parameter, which validates the aforementioned theoretical results. |
| title | Stability transitions of NLS action ground-states on metric graphs |
| topic | Analysis of PDEs Mathematical Physics Classical Analysis and ODEs 34C37, 35B35, 35Q55, 35R02, {37K45}, 70K05 |
| url | https://arxiv.org/abs/2506.23166 |