Pulse Propagation in Chains with Nonlinear Interactions

TL;DR

This paper investigates pulse propagation in nonlinear chains, revealing that traditional dispersion measures can be misleading and providing analytic estimates for energy transfer and pulse velocity in anharmonic systems.

Contribution

It introduces new analytic methods to accurately describe pulse behavior and energy transfer in strongly nonlinear chains, challenging previous dispersion measurement assumptions.

Findings

Traditional dispersion measures can be misleading in nonlinear chains.

Analytic estimates for energy fraction in leading pulses.

Predictions for pulse velocity in Fermi-Pasta-Ulam beta-chain.

Abstract

Pulse propagation in nonlinear arrays continues to be of interest because it provides a possible mechanism for energy transfer with little dispersion. Here we show that common measures of pulse dispersion might be misleading; in strongly anharmonic systems they tend to reflect a succession of extremely narrow pulses traveling at decreasing velocities rather than the actual width of a single pulse. We present analytic estimates for the fraction of the initial energy that travels in the leading pulses. We also provide analytic predictions for the leading pulse velocity in a Fermi-Pasta-Ulam beta-chain.