Equivariant stability of vortices in Manton's Chern-Simons-Schrödinger system on the hyperbolic plane
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915483944484864 |
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| author | Landoulsi, Oussama Shahshahani, Sohrab |
| author_facet | Landoulsi, Oussama Shahshahani, Sohrab |
| contents | In this work we study magnetic vortices on the hyperbolic plane for a Chern-Simons-Schrödinger system introduced by Manton. The model can be thought of as the Schrödinger analogue of the Abalian-Higgs model. It consists of a system of partial differential equations, where the complex Higgs field $Φ$ evolves according to a nonlinear Schrödinger equation coupled to an electromagnetic field $A$. We restrict attention to the self-dual (Bogomolny) case under equivariance symmetry. For each $m\geq 1$ we prove the asymptotic stability of the equivariant vortex of degree $m$. The main novelties are unraveling the favorable structure of the equations after a nonlinear Darboux transform, and the analysis of the elliptic operator relating the original and the transformed variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_06090 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivariant stability of vortices in Manton's Chern-Simons-Schrödinger system on the hyperbolic plane Landoulsi, Oussama Shahshahani, Sohrab Analysis of PDEs In this work we study magnetic vortices on the hyperbolic plane for a Chern-Simons-Schrödinger system introduced by Manton. The model can be thought of as the Schrödinger analogue of the Abalian-Higgs model. It consists of a system of partial differential equations, where the complex Higgs field $Φ$ evolves according to a nonlinear Schrödinger equation coupled to an electromagnetic field $A$. We restrict attention to the self-dual (Bogomolny) case under equivariance symmetry. For each $m\geq 1$ we prove the asymptotic stability of the equivariant vortex of degree $m$. The main novelties are unraveling the favorable structure of the equations after a nonlinear Darboux transform, and the analysis of the elliptic operator relating the original and the transformed variables. |
| title | Equivariant stability of vortices in Manton's Chern-Simons-Schrödinger system on the hyperbolic plane |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.06090 |