On the Uniqueness and Orbital Stability of Slow and Fast Solitary Wave Solutions of the Benjamin Equation
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913340919382016 |
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| author | Abdallah, May Darwich, Mohamad Molinet, Luc |
| author_facet | Abdallah, May Darwich, Mohamad Molinet, Luc |
| contents | This paper is devoted to the study of existence and properties of solitary waves of the Benjamin equation. The studied equation includes a parameter $γ$ in front of the Benjamin-Ono term. We show the existence, uniqueness, decay and orbital stability of solitary wave solutions obtained as a solution to a certain minimization problem, associated either with high speeds without a sign condition on the parameter $γ$ or with low speeds for the appropriate sign. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04711 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Uniqueness and Orbital Stability of Slow and Fast Solitary Wave Solutions of the Benjamin Equation Abdallah, May Darwich, Mohamad Molinet, Luc Analysis of PDEs Mathematical Physics This paper is devoted to the study of existence and properties of solitary waves of the Benjamin equation. The studied equation includes a parameter $γ$ in front of the Benjamin-Ono term. We show the existence, uniqueness, decay and orbital stability of solitary wave solutions obtained as a solution to a certain minimization problem, associated either with high speeds without a sign condition on the parameter $γ$ or with low speeds for the appropriate sign. |
| title | On the Uniqueness and Orbital Stability of Slow and Fast Solitary Wave Solutions of the Benjamin Equation |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2404.04711 |