Long time dynamics and coherent states in nonlinear wave equations

TL;DR

This paper reviews recent advances in identifying all coherent states in nonlinear wave equations, analyzing their stability, and understanding the long-term behavior of solutions close to these states.

Contribution

It provides a comprehensive overview of the classification, stability analysis, and long-term dynamics of coherent states in nonlinear wave equations.

Findings

Identification of all coherent states in certain nonlinear wave equations

Stability criteria for these coherent states

Insights into the long-time behavior of solutions near coherent states

Abstract

We discuss recent progress in finding all coherent states supported by nonlinear wave equations, their stability and the long time behavior of nearby solutions.