# Scattering of radial solutions to the Inhomogeneous Nonlinear Schr\"odinger Equation

## TL;DR

This paper proves scattering for radial solutions of the focusing inhomogeneous nonlinear Schrödinger equation below the mass-energy threshold, extending previous results to a broader parameter range and including the classical case.

## Contribution

It generalizes existing scattering results to a wider set of parameters for the inhomogeneous NLS and introduces a modified approach to handle inhomogeneity.

## Key findings

- Established scattering below the threshold for a broader parameter range.
- Extended the method to the classical NLS case ($b=0$).
- Validated the approach for radial solutions in all intercritical cases.

## Abstract

We prove scattering below the mass-energy threshold for the focusing inhomogeneous nonlinear Schr\"odinger equation \begin{equation} iu_t + \Delta u + |x|^{-b}|u|^{p-1}u=0, \end{equation} when $b \geq 0$ and $N > 2$ in the intercritical case $0 < s_c <1$. This work generalizes the results of Farah and Guzm\'an [9], allowing a broader range of values for the parameters $p$ and $b$. We use a modified version of Dodson-Murphy's approach [6], allowing us to deal with the inhomogeneity. The proof is also valid for the classical nonlinear Schr\"odinger equation ($b = 0$), extending the work in [6] for radial solutions in all intercritical cases.