# Logarithmic Stability for Coefficients Inverse Problem of Coupled Schr\"{o}dinger Equations

## TL;DR

This paper establishes a logarithmic stability estimate for an inverse problem involving coupled Schrödinger equations, using Carleman estimates and Fourier-Bros-Iagolnitzer transform techniques.

## Contribution

It introduces a novel logarithmic stability result for the inverse coefficients problem in coupled Schrödinger equations, employing advanced Carleman estimates and Fourier analysis methods.

## Key findings

- Logarithmic stability estimate derived for the inverse problem.
- Effective use of Carleman estimates for coupled Schrödinger equations.
- Application of Fourier-Bros-Iagolnitzer transform in stability analysis.

## Abstract

In this paper, we study an inverse coefficients problem for two coupled Schr\"{o}dinger equations with an observation of one component of the solution. The observation is done in a nonempty open subset of the domain where the equations hold. A logarithmic type stability result is obtained. The main method is based on the Carleman estimate for coupled Schr\"{o}dinger equations and coupled heatn equations, and the Fourier-Bros-Iagolnitzer transform.