Transition from Solitons to Solitary Waves in the Fermi-Pasta-Ulam Lattice

TL;DR

This paper investigates how solitons in the Fermi-Pasta-Ulam lattice transition into solitary waves as energy increases, analyzing their properties and implications for heat conduction at different temperatures.

Contribution

It provides an analytical and numerical study of the transition from solitons to solitary waves in the Fermi-Pasta-Ulam lattice, highlighting the energy threshold and related behaviors.

Findings

Solitons exist at low energy levels.

Solitary waves form when energy exceeds a threshold.

Transition impacts heat conduction properties.

Abstract

In this paper, we study the smooth transition from solitons to solitary waves in localization, relation between energy and velocity, propagation and scattering property in the Fermi-Pasta-Ulam lattice analytically and numerically. A soliton is a very stable solitary wave that retains its permanent structure after interacting with other solitary waves. A soliton exists when the energy is small, and it becomes a solitary wave when the energy increases to the threshold. The transition could help to understand the distinctly different heat conduction behaviors of the Fermi-Pasta-Ulam lattice at low and high temperature.