Affiliation:
1. CY Cergy Paris University
2. Laboratoire d'Annecy-le-Vieux de Physique Théorique
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 NN-body peakon solution to the Camassa-Holm shallow-water equation depending on two parameters. We present two explicit constructions of a (non-dynamical) rr-matrix formulation for this new Poisson algebra. The first one relies on a tensorization of the NN-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.
Subject
General Physics and Astronomy