# The existence of full dimensional invariant tori for 1-dimensional nonlinear wave equation

## TL;DR

This paper proves the existence and stability of full-dimensional invariant tori with subexponential decay for a 1D nonlinear wave equation, using KAM theory and Bourgain's approach.

## Contribution

It extends KAM theory to establish invariant tori in 1D nonlinear wave equations with external parameters, demonstrating their linear stability.

## Key findings

- Existence of full-dimensional invariant tori with subexponential decay.
- Linear stability of these invariant tori.
- Application of KAM theory and Bourgain's method to nonlinear wave equations.

## Abstract

In this paper we prove the existence and linear stability of full dimensional tori with subexponential decay for 1-dimensional nonlinear wave equation with external parameters, which relies on the method of KAM theory and the idea proposed by Bourgain \cite{BJFA2005}.