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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2201.02920 |
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| _version_ | 1866911870113284096 |
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| author | Damanik, David Li, Yong Xu, Fei |
| author_facet | Damanik, David Li, Yong Xu, Fei |
| contents | This paper studies the existence and uniqueness problem for the generalized Benjamin-Bona-Mahony (gBBM) equation with quasi-periodic initial data on the real line. We obtain an existence and uniqueness result in the classical sense with arbitrary time horizon under the assumption of polynomially decaying initial Fourier data by using the combinatorial analysis method developed in earlier papers by Christ, Damanik-Goldstein, and the present authors. Our result is valid for exponentially decaying initial Fourier data and hence can be viewed as a Cauchy-Kovalevskaya theorem for the gBBM equation with quasi-periodic initial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_02920 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Quasi-Periodic Cauchy Problem for the Generalized Benjamin-Bona-Mahony Equation on the Real Line Damanik, David Li, Yong Xu, Fei Analysis of PDEs Mathematical Physics This paper studies the existence and uniqueness problem for the generalized Benjamin-Bona-Mahony (gBBM) equation with quasi-periodic initial data on the real line. We obtain an existence and uniqueness result in the classical sense with arbitrary time horizon under the assumption of polynomially decaying initial Fourier data by using the combinatorial analysis method developed in earlier papers by Christ, Damanik-Goldstein, and the present authors. Our result is valid for exponentially decaying initial Fourier data and hence can be viewed as a Cauchy-Kovalevskaya theorem for the gBBM equation with quasi-periodic initial data. |
| title | The Quasi-Periodic Cauchy Problem for the Generalized Benjamin-Bona-Mahony Equation on the Real Line |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2201.02920 |