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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2505.06768 |
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| _version_ | 1866915282646204416 |
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| author | Mizumachi, Tetsu |
| author_facet | Mizumachi, Tetsu |
| contents | The $2$-dimensional Toda lattice ($2$D Toda) is a completely integrable semi-discrete wave equation with the KP-II equation in its continuous limit. Using Darboux transformations, we prove the linear stability of $1$-line solitons for $2$D Toda of any size in an exponentially weighted space. We prove that the dominant part of solutions to the linearized equation around a $1$-line soliton is a time derivative of the $1$-line soliton multiplied by a function of time and transverse variables. The amplitude is described by a $1$-dimensional damped wave equation in the transverse variable, as is the case with the linearized KP-II equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06768 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Transverse linear stability of line solitons for 2D Toda Mizumachi, Tetsu Analysis of PDEs Mathematical Physics Exactly Solvable and Integrable Systems Primary, 35B35, 37K40, Secondary, 35Q51 The $2$-dimensional Toda lattice ($2$D Toda) is a completely integrable semi-discrete wave equation with the KP-II equation in its continuous limit. Using Darboux transformations, we prove the linear stability of $1$-line solitons for $2$D Toda of any size in an exponentially weighted space. We prove that the dominant part of solutions to the linearized equation around a $1$-line soliton is a time derivative of the $1$-line soliton multiplied by a function of time and transverse variables. The amplitude is described by a $1$-dimensional damped wave equation in the transverse variable, as is the case with the linearized KP-II equation. |
| title | Transverse linear stability of line solitons for 2D Toda |
| topic | Analysis of PDEs Mathematical Physics Exactly Solvable and Integrable Systems Primary, 35B35, 37K40, Secondary, 35Q51 |
| url | https://arxiv.org/abs/2505.06768 |