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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.26573 |
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| _version_ | 1866913162603790336 |
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| author | Fan, Lili Zhang, Xin Gao, Hongjun |
| author_facet | Fan, Lili Zhang, Xin Gao, Hongjun |
| contents | In this paper, we investigate the modulational stability of periodic traveling waves in a local model for shallow water waves, which is an extended version of the Hunter-Saxton equation. We construct a family of small-amplitude periodic traveling waves for this local model and provide a parameterization of these waves. Using Floquet-Bloch theory, perturbation theory, and spectral analysis, we then establish the modulational stability of these background periodic traveling wave solutions. Finally, we analyze the modulational instability of another extended Hunter-Saxton equation with cubic nonlinearities, following a similar approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26573 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Modulational stability of the periodic traveling wave in a local model for shallow water waves Fan, Lili Zhang, Xin Gao, Hongjun Analysis of PDEs In this paper, we investigate the modulational stability of periodic traveling waves in a local model for shallow water waves, which is an extended version of the Hunter-Saxton equation. We construct a family of small-amplitude periodic traveling waves for this local model and provide a parameterization of these waves. Using Floquet-Bloch theory, perturbation theory, and spectral analysis, we then establish the modulational stability of these background periodic traveling wave solutions. Finally, we analyze the modulational instability of another extended Hunter-Saxton equation with cubic nonlinearities, following a similar approach. |
| title | Modulational stability of the periodic traveling wave in a local model for shallow water waves |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2605.26573 |