Modulational instability of small amplitude periodic traveling waves in the $b$-family of Novikov equation
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866912932373200896 |
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| author | Zhao, Xin Lu, Lin Chen, Aiyong |
| author_facet | Zhao, Xin Lu, Lin Chen, Aiyong |
| contents | We study the modulational instability of smooth, small-amplitude periodic traveling wave solutions to the $b$-family of Novikov equation with cubic nonlinearity with an arbitrary coefficient $b>0$. Our approach is based on applying spectral perturbation theory to the corresponding linearization process. We derive a modulation instability index dependent on the nonlinear parameter $b$ and the fundamental wave number, and prove that when this index is negative, sufficiently small periodic traveling waves in the Novikov equation $b$-family exhibit spectral instability to long-wavelength perturbations. This confirms the well-known Benjamin-Feir instability in the $b$-family of Novikov equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00445 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Modulational instability of small amplitude periodic traveling waves in the $b$-family of Novikov equation Zhao, Xin Lu, Lin Chen, Aiyong Analysis of PDEs Dynamical Systems 35B35, 35C07, 37K45 We study the modulational instability of smooth, small-amplitude periodic traveling wave solutions to the $b$-family of Novikov equation with cubic nonlinearity with an arbitrary coefficient $b>0$. Our approach is based on applying spectral perturbation theory to the corresponding linearization process. We derive a modulation instability index dependent on the nonlinear parameter $b$ and the fundamental wave number, and prove that when this index is negative, sufficiently small periodic traveling waves in the Novikov equation $b$-family exhibit spectral instability to long-wavelength perturbations. This confirms the well-known Benjamin-Feir instability in the $b$-family of Novikov equation. |
| title | Modulational instability of small amplitude periodic traveling waves in the $b$-family of Novikov equation |
| topic | Analysis of PDEs Dynamical Systems 35B35, 35C07, 37K45 |
| url | https://arxiv.org/abs/2603.00445 |