Regularity properties of the cubic biharmonic Schrödinger equation on the half line

In this paper we study the regularity properties of the cubic biharmonic Schrödinger equation posed on the right half line. We prove local well-posedness and obtain a smoothing result in the low-regularity spaces on the half line. In particular we prove that the nonlinear part of the solution on the half line is smoother than the initial data obtaining a full derivative gain in certain cases. Moreover, in the defocusing case, we establish global well-posedness and global smoothing in the higher order regularity spaces by making use of the global-wellposedness result of Özsarı and Yolcu (Commun Pure Appl Phys 18(6):3285–3316, 2019) in the energy space. Also this paper improves the well-posedness result of Özsarı and Yolcu (Commun Pure Appl Phys 18(6):3285–3316, 2019) in the case of cubic nonlinearity.