Orbital stability of Benjamin--Ono multisolitons
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914042949402624 |
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| author | Badreddine, Rana Killip, Rowan Visan, Monica |
| author_facet | Badreddine, Rana Killip, Rowan Visan, Monica |
| contents | We show that multisoliton solutions to the Benjamin--Ono equation are uniformly orbitally stable in $H^s(\mathbb{R})$ for every $-\tfrac12<s\leq \frac12$. This improves the regularity required for stability up to the sharp well-posedness threshold; previous work (even on single solitons) had required $s\geq \frac12$.
One key ingredient in our argument is a new variational characterization of multisolitons. A second ingredient is the extension to low-regularity slowly-decaying solutions of the Wu identity on eigenfunctions of the Lax operator. This extension also allows us to clarify the spectral type of the Lax operator for such potentials by precluding embedded eigenvalues. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14153 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Orbital stability of Benjamin--Ono multisolitons Badreddine, Rana Killip, Rowan Visan, Monica Analysis of PDEs 35Q51 We show that multisoliton solutions to the Benjamin--Ono equation are uniformly orbitally stable in $H^s(\mathbb{R})$ for every $-\tfrac12<s\leq \frac12$. This improves the regularity required for stability up to the sharp well-posedness threshold; previous work (even on single solitons) had required $s\geq \frac12$. One key ingredient in our argument is a new variational characterization of multisolitons. A second ingredient is the extension to low-regularity slowly-decaying solutions of the Wu identity on eigenfunctions of the Lax operator. This extension also allows us to clarify the spectral type of the Lax operator for such potentials by precluding embedded eigenvalues. |
| title | Orbital stability of Benjamin--Ono multisolitons |
| topic | Analysis of PDEs 35Q51 |
| url | https://arxiv.org/abs/2509.14153 |