27 citations · 97 across the 8 of their papers we have counts for
8 papers
Nonlinear Schrödinger equation on the half-line without a conserved number of solitons
Vincent Caudrelier, Nicolas Crampe, Eric Ragoucy +1
We explore the phenomena of absorption/emission of solitons by an integrable boundary for the nonlinear Schrödinger equation on the half-line. This is based on the investigation of…
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…
Exact energy spectrum for models with equally spaced point potentials
V. Caudrelier, N. Crampe
We describe a non-perturbative method for computing the energy band structures of one-dimensional models with general point potentials sitting at equally spaced sites. This is done…