A simple proof of scattering for the intercritical inhomogeneous NLS

TL;DR

This paper presents a straightforward proof of scattering for the intercritical inhomogeneous nonlinear Schrödinger equation below the ground state, leveraging the decay in the nonlinearity to avoid radial assumptions.

Contribution

It provides a simplified proof of scattering for the inhomogeneous NLS without requiring radial symmetry, extending previous methods to a broader class of solutions.

Findings

Proves scattering for intercritical inhomogeneous NLS below the ground state.

Eliminates the need for radial symmetry in the proof.

Uses decay properties of the nonlinearity to simplify the argument.

Abstract

We adapt the argument of Dodson-Murphy to give a simple proof of scattering below the ground state for the intercritical inhomogeneous nonlinear Schr\"odinger equation. The decaying factor in the nonlinearity obviates the need for a radial assumption.