On the instability of the Ruf-Sani solitons for the NLS with exponential nonlinearity

TL;DR

This paper investigates the spectral and blow-up instability of Ruf-Sani solitons in a 2D nonlinear Schrödinger equation with exponential nonlinearity, revealing their inherent instability.

Contribution

It demonstrates the spectral and blow-up instability of Ruf-Sani solitons in the 2D NLS with exponential nonlinearity, extending understanding of their stability properties.

Findings

Ruf-Sani solitons are spectrally unstable.

Ruf-Sani solitons are unstable by blow-up.

The study applies to models with exponential nonlinearity.

Abstract

We study the two dimensional non-linear Schr\"odinger equation with two types of exponential non-linearities. It is well-known by a work of Ruf - Sani, that such models support solitary wave solutions, which are solutions of some constrained minimization problem. We show that these Ruf - Sani solitons, are spectrally unstable as well as unstable by blow-up.