66 citations · 698 across the 60 of their papers we have counts for
62 papers
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…
Elliptic deformation of -algebras
J. Avan, L. Frappat, E. Ragoucy
We construct -deformations of quantum algebras with elliptic structure functions. Their spin generators are built from products of the Lax matrix gene…
From Hamiltonian to zero curvature formulation for classical integrable boundary conditions
Jean Avan, Vincent Caudrelier, Nicolas Crampe
We reconcile the Hamiltonian formalism and the zero curvature representation in the approach to integrable boundary conditions for a classical integrable system in 1+1 space-time d…
Dynamical centers for the elliptic quantum algebra
J. Avan, L. Frappat, E. Ragoucy
We identify generating functionals that satisfy dynamical exchange relations with the Lax matrices defining the face-type elliptic quantum algebra ${\mathcal{B}}_{q,λ}(\hat{gl}_{2}…
On the origin of dual Lax pairs and their -matrix structure
Jean Avan, Vincent Caudrelier
We establish the algebraic origin of the following observations made previously by the authors and coworkers: (i) A given integrable PDE in dimensions within the Zakharov-Sha…