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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.07460 |
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| _version_ | 1866929210161889280 |
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| author | Chen, Robin Ming Fan, Lili Wang, Xingchang Xu, Runzhang |
| author_facet | Chen, Robin Ming Fan, Lili Wang, Xingchang Xu, Runzhang |
| contents | The $b$-family-Kadomtsev-Petviashvili equation ($b$-KP) is a two dimensional generalization of the $b$-family equation. In this paper, we study the spectral stability of the one-dimensional small-amplitude periodic traveling waves with respect to two-dimensional perturbations which are either co-periodic in the direction of propagation, or nonperiodic (localized or bounded). We perform a detailed spectral analysis of the linearized problem associated to the above mentioned perturbations, and derive various stability and instability criteria which depends in a delicate way on the parameter value of $b$, the transverse dispersion parameter $σ$, and the wave number $k$ of the longitudinal waves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07460 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectral analysis of periodic $b$-KP equation under transverse perturbation Chen, Robin Ming Fan, Lili Wang, Xingchang Xu, Runzhang Analysis of PDEs The $b$-family-Kadomtsev-Petviashvili equation ($b$-KP) is a two dimensional generalization of the $b$-family equation. In this paper, we study the spectral stability of the one-dimensional small-amplitude periodic traveling waves with respect to two-dimensional perturbations which are either co-periodic in the direction of propagation, or nonperiodic (localized or bounded). We perform a detailed spectral analysis of the linearized problem associated to the above mentioned perturbations, and derive various stability and instability criteria which depends in a delicate way on the parameter value of $b$, the transverse dispersion parameter $σ$, and the wave number $k$ of the longitudinal waves. |
| title | Spectral analysis of periodic $b$-KP equation under transverse perturbation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.07460 |