Fermi-Pasta-Ulam chains with harmonic and anharmonic long-range interactions

TL;DR

This paper investigates the dynamics of Fermi-Pasta-Ulam chains with long-range harmonic and anharmonic interactions, deriving a generalized fractional Boussinesq equation to describe their continuum limit and exploring models with alternating couplings.

Contribution

It introduces a detailed derivation of a fractional Boussinesq equation for long-range FPU chains and examines models with alternating sign couplings.

Findings

Derivation of a generalized fractional Boussinesq equation for the system

Identification of the continuum limit behavior of long-range interactions

Analysis of models with alternating sign couplings

Abstract

We study the dynamics of Fermi-Pasta-Ulam chains with both harmonic and anharmonic power-law long-range interactions. We show that the dynamics is described in the continuum limit by a generalized fractional Boussinesq differential equation, whose derivation is performed in full detail. We also discuss a version of the model where couplings are alternating in sign.