Energy convexity estimates for non-degenerate ground states of nonlinear 1D Schr\"odinger systems

TL;DR

This paper investigates the spectral properties of linearized operators around ground states in nonlinear Schrödinger systems, revealing their stability and isolation, which are crucial for understanding the dynamics of these systems.

Contribution

It provides new spectral analysis results demonstrating the stability and isolation of non-degenerate ground states in nonlinear Schrödinger systems.

Findings

Ground states are shown to be isolated.

Ground states are orbitally stable.

Spectral properties of the linearized operator are characterized.

Abstract

We study the spectral structure of the complex linearized operator for a class of nonlinear Schr\"odinger systems, obtaining as byproduct some interesting properties of non-degenerate ground state of the associated elliptic system, such as being isolated and orbitally stable.