Stability of standing waves for logarithmic Schr\"odinger equation with attractive delta potential

TL;DR

This paper investigates the stability of standing wave solutions in a one-dimensional logarithmic Schrödinger equation with an attractive delta potential, establishing well-posedness and orbital stability of ground states.

Contribution

It demonstrates global well-posedness in H1 and Orlicz spaces and proves orbital stability of ground states using variational methods.

Findings

Global well-posedness in H1(R) and Orlicz space

Orbital stability of ground states for attractive delta potential

Use of variational approach for stability proof

Abstract

We consider the one-dimensional logarithmic Schr\"odinger equation with a delta potential. Global well-posedness is verified for the Cauchy problem in H1(R) and in an appropriate Orlicz space. In the attractive case, we prove orbital stability of the ground states via variational approach.