Nonlinear steepest descent on a torus: A case study of the Landau-Lifshitz equation
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913773636288512 |
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| author | Desiraju, Harini Its, Alexander R. Prokhorov, Andrei |
| author_facet | Desiraju, Harini Its, Alexander R. Prokhorov, Andrei |
| contents | We obtain rigorous large time asymptotics for the Landau-Lifshitz equation in the soliton free case by extending the nonlinear steepest descent method to genus 1 surfaces. The methods presented in this paper pave the way to a rigorous analysis of other integrable equations on the torus and enable asymptotic analysis on different regimes of the Landau-Lifshitz equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_17662 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonlinear steepest descent on a torus: A case study of the Landau-Lifshitz equation Desiraju, Harini Its, Alexander R. Prokhorov, Andrei Analysis of PDEs Mathematical Physics Exactly Solvable and Integrable Systems 35B40, 35Q15, 35Q51, 35Q60, 37K40, 41A60 We obtain rigorous large time asymptotics for the Landau-Lifshitz equation in the soliton free case by extending the nonlinear steepest descent method to genus 1 surfaces. The methods presented in this paper pave the way to a rigorous analysis of other integrable equations on the torus and enable asymptotic analysis on different regimes of the Landau-Lifshitz equation. |
| title | Nonlinear steepest descent on a torus: A case study of the Landau-Lifshitz equation |
| topic | Analysis of PDEs Mathematical Physics Exactly Solvable and Integrable Systems 35B40, 35Q15, 35Q51, 35Q60, 37K40, 41A60 |
| url | https://arxiv.org/abs/2405.17662 |