Scattering for NLS with a delta potential

TL;DR

This paper proves scattering for the defocusing nonlinear Schrödinger equation with a delta potential in one dimension, extending classical results to an inhomogeneous setting with a supercritical nonlinearity.

Contribution

It extends 1-D scattering results to include a delta potential, addressing inhomogeneous cases with mass-supercritical nonlinearities.

Findings

Established $H^1$ scattering for the model.

Extended classical scattering results to inhomogeneous settings.

Handled mass-supercritical nonlinearities.

Abstract

We prove $H^1$ scattering for defocusing NLS with a delta potential and mass-supercritical nonlinearity, hence extending in an inhomogeneous setting the classical 1-D scattering results first proved by Nakanishi in the translation invariant case.