Scattering below the ground state for the intercritical non-radial inhomogeneous NLS (2007.06165v1)

Abstract: We consider the focusing inhomogeneous nonlinear Schr\"odinger equation [ i\partial_t u + \Delta u + |x|^{-b}|u|^\alpha u = 0\quad\text{on}\quad\mathbb{R}\times\mathbb{R}^N, ] with $N\geq 2$, $0<b<\min{\tfrac{N}{2},2}$, and $\tfrac{4-2b}{N}<\alpha<\tfrac{4-2b}{N-2}$. These constraints make the equation mass-supercritical and energy-subcritical. We extend the results of Farah-Guzm\'an and Miao-Murphy-Zheng and prove scattering below the ground state with general initial data.