Derivation of normal forms for dispersive PDEs via arborification
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909346588262400 |
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| author | Bruned, Yvain |
| author_facet | Bruned, Yvain |
| contents | In this work, we propose a systematic derivation of normal forms for dispersive equations using decorated trees introduced in arXiv:2005.01649. The key tool is the arborification map which is a morphism from the Butcher-Connes-Kreimer Hopf algebra to the Shuffle Hopf algebra. It originates from Ecalle's approach to dynamical systems with singularities. This natural map has been used in many applications ranging from algebra, numerical analysis and rough paths. This connection shows that Hopf algebras also appear naturally in the context of dispersive equations and provide insights into some crucial decomposition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03642 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Derivation of normal forms for dispersive PDEs via arborification Bruned, Yvain Analysis of PDEs Numerical Analysis Probability Rings and Algebras In this work, we propose a systematic derivation of normal forms for dispersive equations using decorated trees introduced in arXiv:2005.01649. The key tool is the arborification map which is a morphism from the Butcher-Connes-Kreimer Hopf algebra to the Shuffle Hopf algebra. It originates from Ecalle's approach to dynamical systems with singularities. This natural map has been used in many applications ranging from algebra, numerical analysis and rough paths. This connection shows that Hopf algebras also appear naturally in the context of dispersive equations and provide insights into some crucial decomposition. |
| title | Derivation of normal forms for dispersive PDEs via arborification |
| topic | Analysis of PDEs Numerical Analysis Probability Rings and Algebras |
| url | https://arxiv.org/abs/2409.03642 |