Y. Komori et K. Hikami, NONLINEAR SCHRODINGER MODEL WITH BOUNDARY, INTEGRABILITY AND SCATTERING MATRIX BASED ON THE DEGENERATE AFFINE HECKE ALGEBRA, International journal of modern physics A, 12(30), 1997, pp. 5397-5410
The delta-function interacting many-body systems (nonlinear Schrodinge
r models) on an infinite interval and with boundary are studied by use
of the integrable differential-difference operators, so-called Dunkl
operators. These models are related with the classical root systems of
type A and BC, and we give a systematic method to construct these int
egrable operators. This method is based on the infinite-dimensional re
presentation for solutions of the classical Yang-Baxter equation and t
he classical reflection equation. In addition the scattering matrices
of the boundary nonlinear Schrodinger model are investigated.