Orbital Stability of Smooth Traveling Solitary Waves to the Fornberg-Whitham Equation
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914580513423360 |
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| author | Deng, Xijun Lafortune, Stephane Liu, Zhisu |
| author_facet | Deng, Xijun Lafortune, Stephane Liu, Zhisu |
| contents | The Fornberg-Whitham (FW) equation was introduced by Fornberg and Whitham [Fornberg and Whitham, Phil. Trans. R. Soc. Lond. A (1978)] as a nonlocal model for unidirectional shallow water waves capable of capturing wave steepening and breaking. Despite its similarities with integrable shallow-water equations, the FW equation is not completely integrable. Nevertheless, the FW equation is part of the family of peakon-type models as it supports peaked traveling wave solutions. In this paper, we consider smooth solitary wave solutions to the FW equation. We use a variational approach to show that some are orbitally stable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19906 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Orbital Stability of Smooth Traveling Solitary Waves to the Fornberg-Whitham Equation Deng, Xijun Lafortune, Stephane Liu, Zhisu Analysis of PDEs Pattern Formation and Solitons Exactly Solvable and Integrable Systems 35C07, 35B35, 37K40, 35Q35 The Fornberg-Whitham (FW) equation was introduced by Fornberg and Whitham [Fornberg and Whitham, Phil. Trans. R. Soc. Lond. A (1978)] as a nonlocal model for unidirectional shallow water waves capable of capturing wave steepening and breaking. Despite its similarities with integrable shallow-water equations, the FW equation is not completely integrable. Nevertheless, the FW equation is part of the family of peakon-type models as it supports peaked traveling wave solutions. In this paper, we consider smooth solitary wave solutions to the FW equation. We use a variational approach to show that some are orbitally stable. |
| title | Orbital Stability of Smooth Traveling Solitary Waves to the Fornberg-Whitham Equation |
| topic | Analysis of PDEs Pattern Formation and Solitons Exactly Solvable and Integrable Systems 35C07, 35B35, 37K40, 35Q35 |
| url | https://arxiv.org/abs/2605.19906 |