An invariant set in energy space for supercritical NLS in 1D

TL;DR

This paper proves the existence of an invariant hypersurface in the energy space for radial solutions of a supercritical 1D nonlinear Schrödinger equation, where solutions converge to ground states.

Contribution

It introduces a new invariant set in energy space for supercritical NLS, demonstrating convergence to ground states for radial solutions.

Findings

Existence of an invariant hypersurface in energy space.

Solutions on this set converge to ground states.

The set is invariant under the NLS flow.

Abstract

We consider radial solutions of a mass supercritical monic NLS and we prove the existence of a set, which looks like a hypersurface, in the space of finite energy functions, invariant for the flow and formed by solutions which converge to ground states.