Hamiltonian field theory close to the wave equation: from Fermi-Pasta-Ulam to water waves
| Autor: | Gallone, Matteo, Ponno, Antonio |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Qualitative Properties of Dispersive PDEs. INdAM 2021. Springer INdAM Series, vol 52. Springer, Singapore (2022) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/978-981-19-6434-3_10 |
| Popis: | In the present work we analyse the structure of the Hamiltonian field theory in the neighbourhood of the wave equation $q_{tt}=q_{xx}$. We show that, restricting to ``graded'' polynomial perturbations in $q_x$, $p$ and their space derivatives of higher order, the local field theory is equivalent, in the sense of the Hamiltonian normal form, to that of the Korteweg-de Vries hierarchy of second order. Within this framework, we explain the connection between the theory of water waves and the Fermi-Pasta-Ulam system. Comment: 37 pages; published version with minor changes. Added some remarks and a concluding sectios |
| Databáze: | arXiv |
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