The initial-boundary value problem for some quadratic nonlinear Schr\"odinger equations on the half-line

Abstract

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.