Existence and stability of solitons for the nonlinear Schr\"odinger equation on hyperbolic space

TL;DR

This paper investigates the existence and stability of solitons for the nonlinear Schrödinger equation on hyperbolic space, showing that results are similar to those in Euclidean space using concentration compactness.

Contribution

It extends the analysis of solitons to hyperbolic space and demonstrates that their existence and stability properties mirror Euclidean space results.

Findings

Existence of ground state solutions on hyperbolic space

Stability properties of these solitons

Method of concentration compactness applies successfully

Abstract

We study the existence and stability of ground state solutions or solitons to a nonlinear stationary equation on hyperbolic space. The method of concentration compactness applies and shows that the results correlate strongly to those of Euclidean space.