The initial-boundary-value problem for the 1D nonlinear Schrödinger equation on the half-line

Abstract

We prove, by adapting the method of Colliander-Kenig [9], local well posedness of the initial-boundary-value problem for the one-dimensional nonlinear Schrödinger equation $i\partial_tu +\partial_x^2u +\lambda u|u|^{\alpha-1}=0$ on the half-line under low boundary regularity assumptions.