Scattering below the ground state for the intercritical non-radial inhomogeneous NLS

Abstract

We consider the focusing inhomogeneous nonlinear Schrödinger equation \[ i\partial_t u + Δu + |x|^{-b}|u|^αu = 0\quad\text{on}\quad\mathbb{R}\times\mathbb{R}^N, \] with $N\ge 2$, $0<b<\min \{\frac{N}{2},2\}$, and $\frac{4-2b}{N}<\hat{I}\pm <\frac{4-2b}{N-2}$. These constraints make the equation mass-supercritical and energy-subcritical. We extend the results of Farah-Guzmán and Miao-Murphy-Zheng and prove scattering below the ground state with general initial data.

20 pages