turkmath.org

In this talk, in broad terms we discuss the initial boundary value problem (IBVP) for the fourth order nonlinear Schrödinger equation (NLS) on the half line. In order to make the audiences familiar with the notions of dispersive equations, we dwell on the defining criteria of this sort of PDE's in the sense of physics (informal definition) and mathematics (more formal one). Afterwards we pass on to the discussion of the celebrated Bourgain spaces for which the concepts of local and global well-posedness are addressed. In the final part we consider the fourth order NLS in the IBVP setting, and mention new well-posedness and regularity results of this higher order Schrödinger type PDE on the half line.