A new integrable structure associated to the Camassa-Holm peakons
Jean Avan, Luc Frappat, Eric Ragoucy
SciPost Phys. 15, 228 (2023) · published 6 December 2023
- doi: 10.21468/SciPostPhys.15.6.228
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Abstract
We provide a closed Poisson algebra involving the Ragnisco-Bruschi generalization of peakon dynamics in the Camassa-Holm shallow-water equation. This algebra is generated by three independent matrices. From this presentation, we propose a one-parameter integrable extension of their structure. It leads to a new $N$-body peakon solution to the Camassa-Holm shallow-water equation depending on two parameters. We present two explicit constructions of a (non-dynamical) $r$-matrix formulation for this new Poisson algebra. The first one relies on a tensorization of the $N$-dimensional auxiliary space by a 4-dimensional space. We identify a family of Poisson commuting quantities in this framework, including the original ones. This leads us to constructing a second formulation identified as a spectral parameter representation.
Cited by 1
Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 Jean Avan,
- 2 Luc Frappat,
- 2 Eric Ragoucy