Scattering of the 2D modified Zakharov-Kuznetsov equation
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915353269895168 |
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| author | Anjolras, Philippe |
| author_facet | Anjolras, Philippe |
| contents | We study the modified Zakharov-Kuznetsov equation in dimension $2$ : \[ \partial_t u + \partial_x \left( Δu + u^3 \right) = 0 \] where $u : (t, (x, y)) \in \mathbb{R} \times \mathbb{R}^2 \mapsto u(t, x, y) \in \mathbb{R}$ and $Δ= \partial_x^2 + \partial_y^2$ is the full Laplacian. We prove that solutions for small and localized initial data scatter for large time. Our proof relies on the method of space-time resonances. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_17179 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scattering of the 2D modified Zakharov-Kuznetsov equation Anjolras, Philippe Analysis of PDEs We study the modified Zakharov-Kuznetsov equation in dimension $2$ : \[ \partial_t u + \partial_x \left( Δu + u^3 \right) = 0 \] where $u : (t, (x, y)) \in \mathbb{R} \times \mathbb{R}^2 \mapsto u(t, x, y) \in \mathbb{R}$ and $Δ= \partial_x^2 + \partial_y^2$ is the full Laplacian. We prove that solutions for small and localized initial data scatter for large time. Our proof relies on the method of space-time resonances. |
| title | Scattering of the 2D modified Zakharov-Kuznetsov equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2506.17179 |