Well-posedness of the initial-boundary value problem for the fourth-order nonlinear Schrödinger equation

The main purpose of this paper is to study local regularity properties of the fourth-order nonlinear Schrodinger equations on the half line. We prove the local existence, uniqueness, and continuous dependence on initial data in low regularity Sobolev spaces. We also obtain the nonlinear smoothing property: the nonlinear part of the solution on the half line is smoother than the initial data.