Existence of Traveling Waves in Infinite Range FPUT Lattices

TL;DR

This paper proves the existence of solitary traveling waves in an infinite-range FPUT lattice with decaying pairwise interactions, using variational methods, and describes their asymptotic behavior at high energies.

Contribution

It introduces a variational approach to establish solitary wave existence in infinite-range lattices with decaying interactions, and characterizes their asymptotic properties.

Findings

Existence of a one-parameter family of solitary waves.

Asymptotic behavior of large, fast, high-energy waves.

Unimodal solutions in an infinite-range interaction lattice.

Abstract

We prove the existence of solitary waves in a lattice where all particles interact with each other by pair-wise repulsive forces that decay with distance. The variational existence proof is based on constrained optimization and provides a one-parameter family of unimodal solutions. We also describe the asymptotic behavior of large, fast, high-energy waves.