Scattering for the non-radial focusing inhomogeneous nonlinear Schrödinger-Choquard equation

Abstract

In this paper, we study the long-time behavior of global solutions to the Schrödinger-Choquard equation $$i{\partial }_{t}u+\Delta u=-(I_{\alpha }\ast |\cdot {|}^b|u{|}^p)|\cdot {|}^b|u{|}^{p-2}u.$$ Inspired by Murphy, who gave a simple proof of scattering for the non-radial inhomogeneous NLS, we prove scattering theory below the ground state for the intercritical case in energy space without radial assumption.