An integrable generalization of the nonlinear Schr\"odinger equation on   the half-line and solitons
  We analyze initial-boundary value problems for an integrable generalization of the nonlinear Schr\"odinger equation formulated on the half-line. In particular, we investigate the so-called linearizable boundary conditions, which in this case are of Robin type. Furthermore, we use a particular solution to verify explicitly all the steps needed for the solution of a well-posed problem. 
J. Lenells and A. S. Fokas