Quantization of the Nonlinear Schrodinger Equation on the Half Line
  We establish the second quantized solution of the nonlinear Schrodinger equation on the half line with a mixed boundary condition. The solution is based on a new algebraic structure, which we call boundary exchange algebra and which substitutes, in the presence of boundaries, the familiar Zamolodchikov-Faddeev algebra. 
M. Gattobigio (INFN, Pisa & Pisa U.), A. Liguori (ISAAS, Trieste), M.   Mintchev (INFN, Pisa & Pisa U.)