The initial-boundary value problem for some quadratic nonlinear   Schr\"odinger equations on the half-line
  We prove local well-posedness for the initial-boundary-value problem associated to some quadratic nonlinear Schr\"odinger equations on the half-line. The results are obtained in the low regularity setting by introducing an analytic family of boundary forcing operators, following the ideas developed by Colliander, Kenig and Holmer. 
M\'arcio Cavalcante
math.AP