Scattering for the \({1d}\) NLS with Inhomogeneous Nonlinearities

Abstract

Abstract. We prove large-data scattering in [Formula: see text] for inhomogeneous nonlinear Schrödinger equations in one space dimension for powers [Formula: see text]. We assume the inhomogeneity is nonnegative and repulsive; we additionally require decay at infinity in the case [Formula: see text]. We use the method of concentration-compactness and contradiction, utilizing a Morawetz estimate in the style of Nakanishi in order to preclude the existence of compact solutions.