# Analytic solutions of nonlinear elliptic equations on rectangular tori

## TL;DR

This paper demonstrates the existence of numerous analytic solutions to nonlinear elliptic equations on rectangular tori by employing techniques from KAM theory and Anderson localization.

## Contribution

It introduces a novel approach combining KAM theory and Anderson localization to find analytic solutions for nonlinear elliptic equations on rectangular tori.

## Key findings

- Existence of many analytic solutions on rectangular tori.
- Application of KAM theory and Anderson localization methods.
- Advancement in understanding nonlinear elliptic equations.

## Abstract

In this paper, we consider the nonlinear elliptic equations on rectangular tori. Using methods in the study of KAM theory and Anderson localization, we prove that these equations admit many analytic solutions.