27 citations · 97 across the 8 of their papers we have counts for
5 papers · 1 filter
New integrable boundary conditions for the Ablowitz-Ladik model: from Hamiltonian formalism to nonlinear mirror image method
Vincent Caudrelier, Nicolas Crampe
Using Sklyanin's classical theory of integrable boundary conditions, we use the Hamiltonian approach to derive new integrable boundary conditions for the Ablowitz-Ladik model on th…
Classical -Reflection Equation and Gaudin Models
Vincent Caudrelier, Nicolas Crampe
We introduce the notion of -reflection equation which provides a large generalization of the usual classical reflection equation describing integrable boundary conditions. The l…
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…
Set-theoretical reflection equation: Classification of reflection maps
V. Caudrelier, N. Crampe, Q. C. Zhang
The set-theoretical reflection equation and its solutions, the reflection maps, recently introduced by two of the authors, is presented in general and then applied in the context o…
Integrable N-particle Hamiltonians with Yangian or Reflection Algebra Symmetry
V. Caudrelier, N. Crampe
We use the Dunkl operator approach to construct one dimensional integrable models describing N particles with internal degrees of freedom. These models are described by a general H…