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PreprintCC BY 4.0arXiv

On the integrability of the Kirchhoff-Pohozaev equation on tori

  • Dario Bambusi
  • Emanuele Haus
  • Simone Marrocco
  • Michela Procesi
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Abstract

In this paper we study the Kirchhoff-Pohozaev equation introduced in \cite{P2} and its constants of motion (see \cite{BoitiManfrin2025}, \cite{BoitiManfrin2026}) on n dimensional tori. We show that these Hamiltonians are all in involution and we prove that they are generated by an infinite list of constants of motion which are all defined and in involution on a fixed phase space. Then we study the Kirchhoff-Pohozaev equation restricted to a finite Fourier support. In dimension n=1 we show that such finite dimensional reduction is always completely integrable and provide an analytic Brikhoff normal form in a neighborhood of the origin. We also give sufficient conditions for integrability for n>1. We finally show that the formal Birkhoff Normal form of the Kirchhoff-Pohozaev equation is integrable for n=1.

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Cite

BibTeXRIS
BibTeX
@misc{bambusi2026integrability,
  title = {{On the integrability of the Kirchhoff-Pohozaev equation on tori}},
  author = {Dario Bambusi and Emanuele Haus and Simone Marrocco and Michela Procesi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.01891},
  eprint = {2609.01891},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.01891},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On the integrability of the Kirchhoff-Pohozaev equation on tori
AU  - Dario Bambusi
AU  - Emanuele Haus
AU  - Simone Marrocco
AU  - Michela Procesi
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.01891
UR  - https://arxiv.org/abs/2609.01891
AB  - In this paper we study the Kirchhoff-Pohozaev equation introduced in \cite{P2} and its constants of motion (see \cite{BoitiManfrin2025}, \cite{BoitiManfrin2026}) on n dimensional tori. We show that these Hamiltonians are all in involution and we prove that they are generated by an infinite list of constants of motion which are all defined and in involution on a fixed phase space. Then we study the Kirchhoff-Pohozaev equation restricted to a finite Fourier support. In dimension n=1 we show that such finite dimensional reduction is always completely integrable and provide an analytic Brikhoff normal form in a neighborhood of the origin. We also give sufficient conditions for integrability for n>1. We finally show that the formal Birkhoff Normal form of the Kirchhoff-Pohozaev equation is integrable for n=1.
ER  -