TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.6.228
TI  - A new integrable structure associated to the Camassa-Holm peakons
PY  - 2023/12/06
UR  - https://www.scipost.org/SciPostPhys.15.6.228
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 6
SP  - 228
A1  - Avan, Jean
AU  - Frappat, Luc
AU  - Ragoucy, Eric
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.15.6.228,
	title={{A new integrable structure associated to the Camassa-Holm peakons}},
	author={Jean Avan and Luc Frappat and Eric Ragoucy},
	journal={SciPost Phys.},
	volume={15},
	pages={228},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.6.228},
	url={https://scipost.org/10.21468/SciPostPhys.15.6.228},
}