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Quadratic Poisson brackets for the Camassa--Holm peakons
J. Avan, L. Frappat, E. Ragoucy
We establish quadratic Poisson brackets for the generalized Camassa--Holm peakon structure introduced in \cite{AFR23}. The calculation is based on the halving of the spectral param…
A new integrable structure associated to the Camassa-Holm peakons
J. Avan, L. Frappat, E. Ragoucy
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 thre…
Integrable quadratic structures in peakon models
J. Avan, L. Frappat, E. Ragoucy
We propose realizations of the Poisson structures for the Lax representations of three integrable -body peakon equations, Camassa--Holm, Degasperis--Procesi and Novikov. The Poi…
Algebraic structure of classical integrability for complex sine-Gordon
J. Avan, L. Frappat, E. Ragoucy
The algebraic structure underlying the classical -matrix formulation of the complex sine-Gordon model is fully elucidated. It is characterized by two matrices and , compo…