Orbital stability of Gausson solutions to logarithmic Schr\"odinger equations

TL;DR

This paper proves the orbital stability of ground state solutions to the logarithmic Schrödinger equation across any dimension, including cases with nonradial perturbations, advancing understanding of their long-term behavior.

Contribution

It provides the first proof of orbital stability for ground states of the logarithmic Schrödinger equation in arbitrary dimensions with nonradial perturbations.

Findings

Ground state solutions are orbitally stable in any dimension.

Stability holds even under nonradial perturbations.

The proof extends previous results limited to radial cases.

Abstract

In this paper we present a proof of the orbital stability of ground state for logarithmic Schr\"odinger equation in any dimension and under nonradial perturbations.