Some breathers and multi-breathers for FPU-type chains

TL;DR

This paper proves the existence and stability of numerically found breather solutions in FPU chains using computer-assisted methods, and explores their symmetry and superposition properties.

Contribution

It introduces computer-assisted proofs for breather solutions in FPU chains and analyzes their stability and symmetry, advancing understanding of nonlinear lattice dynamics.

Findings

Existence of true breather solutions near numerical approximations

Spectral stability determined for some solutions

Construction of solutions close to sums of breathers

Abstract

We consider several breather solutions for FPU-type chains that have been found numerically. Using computer-assisted techniques, we prove that there exist true solutions nearby, and in some cases, we determine whether or not the solution is spectrally stable. Symmetry properties are considered as well. In addition, we construct solutions that are close to (possibly infinite) sums of breather solutions.