27 citations · 91 across the 8 of their papers we have counts for
5 papers · 1 filter
Reflection Maps Associated with Involutions and Factorization Problems, and Their Poisson Geometry
Luen-Chau Li, Vincent Caudrelier
The study of the set-theoretic solutions of the reflection equation, also known as reflection maps, is closely related to that of the Yang-Baxter maps. In this work, we construct r…
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…
Yang-Baxter and reflection maps from vector solitons with a boundary
V. Caudrelier, Q. C. Zhang
Based on recent results obtained by the authors on the inverse scattering method of the vector nonlinear Schrödinger equation with integrable boundary conditions, we discuss the fa…
Vector Nonlinear Schrödinger Equation on the half-line
V. Caudrelier, Q. C. Zhang
We investigate the Manakov model or, more generally, the vector nonlinear Schrödinger equation on the half-line. Using a Bäcklund transformation method, two classes of integrable b…
Solving the quantum non-linear Schrodinger equation with delta-type impurity
V. Caudrelier, M. Mintchev, E. Ragoucy
We establish the exact solution of the nonlinear Schrodinger equation with a delta-function impurity, representing a point-like defect which reflects and transmits. We solve the pr…