The phase plane of moving discrete breathers

TL;DR

This paper investigates localized vibrational modes called breathers in a five-atom chain with anharmonic springs, analyzing their stability, motion, and transition to chaos using phase plane visualization and symmetry techniques.

Contribution

It introduces a method to visualize the phase plane of breathers and explores their stability and chaotic behavior in a nonlinear atomic chain.

Findings

Long-lived breathers can move chaotically.

A transition to chaos prevents moving breathers at high energies.

Symmetry-based techniques simplify finding periodic orbits.

Abstract

We study anharmonic localization in a periodic five atom chain with quadratic-quartic spring potential. We use discrete symmetries to eliminate the degeneracies of the harmonic chain and easily find periodic orbits. We apply linear stability analysis to measure the frequency of phonon-like disturbances in the presence of breathers and to analyze the instabilities of breathers. We visualize the phase plane of breather motion directly and develop a technique for exciting pinned and moving breathers. We observe long-lived breathers that move chaotically and a global transition to chaos that prevents forming moving breathers at high energies.