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| Main Authors: | , |
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| Format: | Preprint |
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2023
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| Online Access: | https://arxiv.org/abs/2308.06381 |
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| _version_ | 1866909524984594432 |
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| author | Perry, Peter Schuetz, Camille |
| author_facet | Perry, Peter Schuetz, Camille |
| contents | The fifth-order KP II equation $$ \partial_t u + α\partial_x^3 u + β\partial_x^5 u + u \partial_x u + \partial_x^{-1} \partial_y^2u=0$$ ($β<0$, $α>0$) is a nonlinear dispersive equation that models long dispersive waves in two space dimensions. We prove that solutions of the fifth-order KP II equation scatter to solutions of the corresponding linear equation $$ \partial_t v + α\partial_x^3 v + β\partial_x^5 v + \partial_x^{-1} \partial_y^2 v = 0$$ for small data. Our proof uses builds on Hadac, Herr, and Koch's work (see ArXiv:0708.2011) on the third-order KP II equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_06381 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Solutions to the Fifth-Order KP II Equation Scatter Perry, Peter Schuetz, Camille Analysis of PDEs 35Q53, 35P25 The fifth-order KP II equation $$ \partial_t u + α\partial_x^3 u + β\partial_x^5 u + u \partial_x u + \partial_x^{-1} \partial_y^2u=0$$ ($β<0$, $α>0$) is a nonlinear dispersive equation that models long dispersive waves in two space dimensions. We prove that solutions of the fifth-order KP II equation scatter to solutions of the corresponding linear equation $$ \partial_t v + α\partial_x^3 v + β\partial_x^5 v + \partial_x^{-1} \partial_y^2 v = 0$$ for small data. Our proof uses builds on Hadac, Herr, and Koch's work (see ArXiv:0708.2011) on the third-order KP II equation. |
| title | Solutions to the Fifth-Order KP II Equation Scatter |
| topic | Analysis of PDEs 35Q53, 35P25 |
| url | https://arxiv.org/abs/2308.06381 |