# Exponential stability for the nonlinear Schr\"odinger equation on a star-shaped network

## TL;DR

This paper proves that solutions to a nonlinear dissipative Schr"odinger equation on a star-shaped network decay exponentially over time, with damping localized on one branch and at infinity.

## Contribution

It establishes exponential stability for the nonlinear Schr"odinger equation on a star-shaped network with localized damping, a novel result in this setting.

## Key findings

- Exponential decay of solutions proven
- Stability holds with damping on one branch and at infinity
- Advances understanding of nonlinear Schr"odinger dynamics on networks

## Abstract

In this paper, we prove the exponential stability of the solution of the nonlinear dissipative Schr\"odinger equation on a star-shaped network and where the damping is localized on one branch and at the infinity.