Stability of Nonlinear Normal Modes in the FPU-$\beta$ Chain in the Thermodynamic Limit

TL;DR

This paper investigates the stability of symmetry-determined nonlinear normal modes in the FPU-β chain, providing a general method applicable in the thermodynamic limit and analyzing both hard and soft potential cases.

Contribution

It introduces a general approach for stability analysis of nonlinear normal modes in large FPU-β chains, applicable to both hard and soft potentials.

Findings

Stability properties of nonlinear normal modes are characterized.

A general method for stability analysis in the thermodynamic limit is developed.

Applications to specific modes demonstrate the method's effectiveness.

Abstract

All possible symmetry-determined nonlinear normal modes (also called by simple periodic orbits, one-mode solutions etc.) in both hard and soft Fermi-Pasta-Ulam-$\beta$ chains are discussed. A general method for studying their stability in the thermodynamic limit, as well as its application for each of the above nonlinear normal modes are presented.