Micropterons, Nanopterons and Solitary Wave Solutions to the Diatomic Fermi-Pasta-Ulam-Tsingou Problem

TL;DR

This paper numerically investigates traveling wave solutions in the diatomic FPUT problem, revealing connections between micropterons, nanopterons, and solitary waves, and demonstrating their stability.

Contribution

It introduces a specialized numerical solver and continuation method to explore the solution landscape, uncovering new relationships and stability properties of wave solutions.

Findings

Micropterons and nanopterons are interconnected in the solution space.

Diatomic solitary waves are numerically shown to be stable.

The solution surfaces form a nontrivial connected structure.

Abstract

We use a specialized boundary-value problem solver for mixed-type functional differential equations to numerically examine the landscape of traveling wave solutions to the diatomic Fermi-Pasta-Ulam-Tsingou (FPUT) problem. By using a continuation approach, we are able to uncover the relationship between the branches of micropterons and nanopterons that have been rigorously constructed recently in various limiting regimes. We show that the associated surfaces are connected together in a nontrivial fashion and illustrate the key role that solitary waves play in the branch points. Finally, we numerically show that the diatomic solitary waves are stable under the full dynamics of the FPUT system.