Asymptotic stability of fast solitary waves to the Benjamin Equation
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917346137866240 |
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| author | Abdallah, May Darwich, Mohamad Molinet, Luc |
| author_facet | Abdallah, May Darwich, Mohamad Molinet, Luc |
| contents | We prove the asymptotic stability of the high speed solitary waves to the Benjamin equation. This is done by establishing a Liouville property for the nonlinear evolution of the Benjamin equation around these solitary waves. To do this, inspired by Kenig-Martel-Robbiano 2011, we make use of the KdV limit of the Benjamin equation together with known rigidity property of the KdV flow. The main difficulties are linked to the presence of the Hilbert transform, that is a non-local operator, as well as the non-positivity of the quadratic part of the energy in the case $ γ<0$ which is the physical case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_17846 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic stability of fast solitary waves to the Benjamin Equation Abdallah, May Darwich, Mohamad Molinet, Luc Analysis of PDEs 35B40, 35B53, 35Q53, 35Q35 We prove the asymptotic stability of the high speed solitary waves to the Benjamin equation. This is done by establishing a Liouville property for the nonlinear evolution of the Benjamin equation around these solitary waves. To do this, inspired by Kenig-Martel-Robbiano 2011, we make use of the KdV limit of the Benjamin equation together with known rigidity property of the KdV flow. The main difficulties are linked to the presence of the Hilbert transform, that is a non-local operator, as well as the non-positivity of the quadratic part of the energy in the case $ γ<0$ which is the physical case. |
| title | Asymptotic stability of fast solitary waves to the Benjamin Equation |
| topic | Analysis of PDEs 35B40, 35B53, 35Q53, 35Q35 |
| url | https://arxiv.org/abs/2410.17846 |