Global perturbation of isolated equivariant chiral skyrmions from the Bogomol'nyi case
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912921612713984 |
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| author | Ibrahim, Slim Shimizu, Ikkei |
| author_facet | Ibrahim, Slim Shimizu, Ikkei |
| contents | Isolated skyrmion solutions to the two-dimensional Landau-Lifshitz equation with Dzyaloshinskii-Moriya interaction, Zeeman term, and easy-plane anisotropy of various strengths are studied. In the full range of parameter values for which the energy is a positive variation of the Bogomol'nyi case, we construct solutions to the corresponding Euler-Lagrange equation and analyze their qualitative properties, including monotonicity, exponential decay, and stability. Our analysis is global and non-perturbative. Moreover, we derive precise estimates qualifying the difference between these solutions and those in the Bogomol'nyi regime. A key ingredient of our approach is a novel resolvent estimate for the linearized operator, which remains uniform with respect to additional implicit potentials arising in the problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03209 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global perturbation of isolated equivariant chiral skyrmions from the Bogomol'nyi case Ibrahim, Slim Shimizu, Ikkei Analysis of PDEs 35B25, 35C08, 49S05, 82D40 Isolated skyrmion solutions to the two-dimensional Landau-Lifshitz equation with Dzyaloshinskii-Moriya interaction, Zeeman term, and easy-plane anisotropy of various strengths are studied. In the full range of parameter values for which the energy is a positive variation of the Bogomol'nyi case, we construct solutions to the corresponding Euler-Lagrange equation and analyze their qualitative properties, including monotonicity, exponential decay, and stability. Our analysis is global and non-perturbative. Moreover, we derive precise estimates qualifying the difference between these solutions and those in the Bogomol'nyi regime. A key ingredient of our approach is a novel resolvent estimate for the linearized operator, which remains uniform with respect to additional implicit potentials arising in the problem. |
| title | Global perturbation of isolated equivariant chiral skyrmions from the Bogomol'nyi case |
| topic | Analysis of PDEs 35B25, 35C08, 49S05, 82D40 |
| url | https://arxiv.org/abs/2503.03209 |