Scattering problem for the generalized Korteweg-de Vries equation
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910550383919104 |
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| author | Masaki, Satoshi Segata, Jun-ichi |
| author_facet | Masaki, Satoshi Segata, Jun-ichi |
| contents | In this paper we study the scattering problem for the initial value problem of the generalized Korteweg-de Vries (gKdV) equation. The purpose of this paper is to achieve two primary goals. Firstly, we show small data scattering for (gKdV) in the weighted Sobolev space, ensuring the initial and the asymptotic states belong to the same class. Secondly, we introduce two equivalent characterizations of scattering in the weighted Sobolev space. In particular, this involves the so-called conditional scattering in the weighted Sobolev space. A key ingredient is incorporation of the scattering criterion for (gKdV) in the Fourier-Lebesgue space by the authors into the the scattering problem in the weighted Sobolev space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00261 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scattering problem for the generalized Korteweg-de Vries equation Masaki, Satoshi Segata, Jun-ichi Analysis of PDEs Primary 35Q53, 35B40, Secondary 35B30 In this paper we study the scattering problem for the initial value problem of the generalized Korteweg-de Vries (gKdV) equation. The purpose of this paper is to achieve two primary goals. Firstly, we show small data scattering for (gKdV) in the weighted Sobolev space, ensuring the initial and the asymptotic states belong to the same class. Secondly, we introduce two equivalent characterizations of scattering in the weighted Sobolev space. In particular, this involves the so-called conditional scattering in the weighted Sobolev space. A key ingredient is incorporation of the scattering criterion for (gKdV) in the Fourier-Lebesgue space by the authors into the the scattering problem in the weighted Sobolev space. |
| title | Scattering problem for the generalized Korteweg-de Vries equation |
| topic | Analysis of PDEs Primary 35Q53, 35B40, Secondary 35B30 |
| url | https://arxiv.org/abs/2408.00261 |