Sharp threshold of scattering versus non-scattering for some mass-sub-critical inhomogeneous NLS

TL;DR

This paper establishes a precise threshold determining whether solutions to certain inhomogeneous mass-subcritical nonlinear Schrödinger equations scatter or not over long times, depending on the source term.

Contribution

It provides the first sharp threshold criterion for scattering versus non-scattering in inhomogeneous mass-subcritical NLS equations.

Findings

Identifies a sharp threshold for scattering behavior

Characterizes the influence of the source term on long-term dynamics

Complements existing literature on inhomogeneous NLS

Abstract

This work investigates the long time asymptotic behavior of some inhomogeneous non-linear Schr\"odinger type equations. We give sharp a threshold of scattering versus non-scattering of mass solutions, depending on the source term. This work complements the literature to the inhomogeneous regime.