The quantum non-linear Schrodinger model with point-like defect
  We establish a family of point-like impurities which preserve the quantum integrability of the non-linear Schrodinger model in 1+1 space-time dimensions. We briefly describe the construction of the exact second quantized solution of this model in terms of an appropriate reflection-transmission algebra. The basic physical properties of the solution, including the space-time symmetry of the bulk scattering matrix, are also discussed. 
V. Caudrelier, M. Mintchev and E. Ragoucy