Self-similar solutions for the generalized fractional Korteweg-de Vries equation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910652219523072 |
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| author | Molinet, Luc Vento, Stéphane Weissler, Fred |
| author_facet | Molinet, Luc Vento, Stéphane Weissler, Fred |
| contents | We consider the Cauchy problem for the generalized fractional Korteweg-de Vries equation $$ u_t+D^αu_x + u^p u_x= 0, \quad 1<α\le 2, \quad p\in {\mathbb N}\setminus\{0\}, $$ with homogeneous initial data $Φ$. We show that, under smallness assumption on $Φ$, and for a wide range of $(α, p)$, including $p=3$, we can construct a self-similar solution of this problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_12063 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Self-similar solutions for the generalized fractional Korteweg-de Vries equation Molinet, Luc Vento, Stéphane Weissler, Fred Analysis of PDEs 35C06, 35Q53, 35Q35 We consider the Cauchy problem for the generalized fractional Korteweg-de Vries equation $$ u_t+D^αu_x + u^p u_x= 0, \quad 1<α\le 2, \quad p\in {\mathbb N}\setminus\{0\}, $$ with homogeneous initial data $Φ$. We show that, under smallness assumption on $Φ$, and for a wide range of $(α, p)$, including $p=3$, we can construct a self-similar solution of this problem. |
| title | Self-similar solutions for the generalized fractional Korteweg-de Vries equation |
| topic | Analysis of PDEs 35C06, 35Q53, 35Q35 |
| url | https://arxiv.org/abs/2410.12063 |