Symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line II
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908278515040256 |
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| author | Wilczak, Daniel Zgliczyński, Piotr |
| author_facet | Wilczak, Daniel Zgliczyński, Piotr |
| contents | We prove the existence of infinite number of homoclinic and heteroclinic orbits to two periodic orbits for the Kuramoto-Sivashinsky PDE on the line with odd and periodic boundary conditions and for some fixed parameter value of the system. The proof is computer assisted and it is based on a new algorithm for rigorous integration of the variational equation for a class of dissipative PDEs on the torus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_17087 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line II Wilczak, Daniel Zgliczyński, Piotr Dynamical Systems Numerical Analysis Analysis of PDEs 35B40, 65G40, 35B30, 35B10, 35B45, 65N30 We prove the existence of infinite number of homoclinic and heteroclinic orbits to two periodic orbits for the Kuramoto-Sivashinsky PDE on the line with odd and periodic boundary conditions and for some fixed parameter value of the system. The proof is computer assisted and it is based on a new algorithm for rigorous integration of the variational equation for a class of dissipative PDEs on the torus. |
| title | Symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line II |
| topic | Dynamical Systems Numerical Analysis Analysis of PDEs 35B40, 65G40, 35B30, 35B10, 35B45, 65N30 |
| url | https://arxiv.org/abs/2405.17087 |