Variational methods for breather solutions of Nonlinear Wave Equations

TL;DR

This paper develops a variational framework to construct infinitely many localized, time-periodic breather solutions for nonlinear wave equations, including Klein-Gordon and biharmonic types.

Contribution

It introduces a novel variational approach to find breather solutions for a broad class of nonlinear wave equations, extending existing methods.

Findings

Existence of infinitely many breather solutions

Solutions are weakly localized in space

Framework applicable to Klein-Gordon and biharmonic wave equations

Abstract

We construct infinitely many real-valued, time-periodic breather solutions of power-type nonlinear wave equations. These solutions are obtained from critical points of a dual functional and they are weakly localized in space. Our abstract framework allows to find similar existence results for the Klein-Gordon equation or biharmonic wave equations.