Solitons as candidates for energy carriers in Fermi-Pasta-Ulam lattices

TL;DR

This paper demonstrates that solitons are viable energy carriers in Fermi-Pasta-Ulam lattices by comparing theoretical soliton velocities with numerical results, showing strong agreement and challenging the dominance of effective phonons.

Contribution

It introduces a method to evaluate soliton velocities using approximate solutions and Boltzmann distribution, establishing solitons as credible energy carriers in nonlinear lattices.

Findings

Soliton velocities match numerical results and existing theories.

Solitons are suitable energy carriers in FPU lattices.

Root-mean-square velocity of solitons derived from phonon theory.

Abstract

Currently, effective phonons (renormalized or interacting phonons) rather than solitary waves (for short, solitons) are regarded as the energy carriers in nonlinear lattices. In this work, by using the approximate soliton solutions of the corresponding equations of motion and adopting the Boltzmann distribution for these solitons, the average velocities of solitons are obtained and are compared with the sound velocities of energy transfer. Excellent agreements with the numerical results and the predictions of other existing theories are shown in both the symmetric Fermi-Pasta-Ulam-$\beta$ lattices and the asymmetric Fermi-Pasta-Ulam-$\alpha \beta$ lattices. These clearly indicate that solitons are suitable candidates for energy carriers in Fermi-Pasta-Ulam lattices. In addition, the root-mean-square velocity of solitons can be obtained from the effective phonons theory.