Global Well-Posedness for the Fourth-Order Nonlinear Schrödinger Equation

Abstract.

The local and global well-posedness for the one dimensional fourth-order nonlinear Schrödinger equation are established in the modulation space [Formula: see text] for [Formula: see text] and [Formula: see text]. The local result is based on the [Formula: see text] spaces and crucial bilinear estimates. The key ingredient to obtain the global well-posedness is that we achieve a priori estimates of the solution in modulation spaces by utilizing the power series expansion of the perturbation determinant introduced by Killip–Vişan–Zhang for completely integrable PDEs.