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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.00436 |
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| _version_ | 1866912458934845440 |
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| author | Song, Peifei Xie, Yuhao Chen, Min Li, Shenghao |
| author_facet | Song, Peifei Xie, Yuhao Chen, Min Li, Shenghao |
| contents | We continue the study for standing wave solutions of $abcd$-systems which was started by Chen and Iooss \cite{chen2005standing} for the BBM system via the Lyapunov-Schmidt method. In this paper, we will first discuss the feasibility of the Lyapunov-Schmidt method for bifurcating standing wave solutions of $abcd$-systems. These systems will be characterized into three categories: feasible, infeasible and uncertain feasible ones. In particular, we prove the existence of nontrivial bifurcating standing waves for the Bona-Smith system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00436 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Standing wave solutions of $abcd$-systems for water waves Song, Peifei Xie, Yuhao Chen, Min Li, Shenghao Analysis of PDEs 35Q35, 35G25, 35D30 We continue the study for standing wave solutions of $abcd$-systems which was started by Chen and Iooss \cite{chen2005standing} for the BBM system via the Lyapunov-Schmidt method. In this paper, we will first discuss the feasibility of the Lyapunov-Schmidt method for bifurcating standing wave solutions of $abcd$-systems. These systems will be characterized into three categories: feasible, infeasible and uncertain feasible ones. In particular, we prove the existence of nontrivial bifurcating standing waves for the Bona-Smith system. |
| title | Standing wave solutions of $abcd$-systems for water waves |
| topic | Analysis of PDEs 35Q35, 35G25, 35D30 |
| url | https://arxiv.org/abs/2507.00436 |