Small Generalized Breathers with Exponentially Small Tails for Klein-Gordon Equations

TL;DR

This paper demonstrates the existence of small, localized oscillatory solutions called breathers with exponentially small tails in a class of nonlinear Klein-Gordon equations, expanding understanding of their behavior.

Contribution

It proves the generic existence of small breathers with exponentially small tails in nonlinear Klein-Gordon equations, a significant theoretical advancement.

Findings

Existence of small breathers with exponentially small tails

Generic conditions for breathers in Klein-Gordon equations

Theoretical framework for localized oscillatory solutions

Abstract

We consider a class of nonlinear Klein-Gordon equation $u_{tt}=u_{xx}-u+f(u)$ and show that generically there exist small breathers with exponentially small tails.