A proof of the soliton resolution conjecture for the Benjamin--Ono equation
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917205640216576 |
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| author | Gassot, Louise Gérard, Patrick Miller, Peter D. |
| author_facet | Gassot, Louise Gérard, Patrick Miller, Peter D. |
| contents | We give a proof of the soliton resolution conjecture for the Benjamin--Ono equation, namely every solution with sufficiently regular and decaying initial data can be written as a finite sum of soliton solutions with different velocities up to a radiative remainder term in the long--time asymptotics. We provide a detailed correspondence between the spectral theory of the Lax operator associated to the initial data and the different terms of the soliton resolution expansion. The proof is based on a new use of a representation formula of the solution due to the second author, and on a detailed analysis of the distorted Fourier transform associated to the Lax operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10488 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A proof of the soliton resolution conjecture for the Benjamin--Ono equation Gassot, Louise Gérard, Patrick Miller, Peter D. Analysis of PDEs 37K10, 35B40, 35Q51 We give a proof of the soliton resolution conjecture for the Benjamin--Ono equation, namely every solution with sufficiently regular and decaying initial data can be written as a finite sum of soliton solutions with different velocities up to a radiative remainder term in the long--time asymptotics. We provide a detailed correspondence between the spectral theory of the Lax operator associated to the initial data and the different terms of the soliton resolution expansion. The proof is based on a new use of a representation formula of the solution due to the second author, and on a detailed analysis of the distorted Fourier transform associated to the Lax operator. |
| title | A proof of the soliton resolution conjecture for the Benjamin--Ono equation |
| topic | Analysis of PDEs 37K10, 35B40, 35Q51 |
| url | https://arxiv.org/abs/2601.10488 |