# Nanoptera and Stokes Curves in the 2-Periodic Fermi-Pasta-Ulam-Tsingou Equation

## TL;DR

This paper investigates nonlocal solitary waves called nanoptera in a period-2 FPUT lattice, using exponential asymptotics to analyze wave trains and identify conditions for localized solutions, validated by numerical simulations.

## Contribution

It introduces an exponential asymptotic method to analyze nanoptera and Stokes curves in the 2-periodic FPUT equation, revealing conditions for localized solitary waves.

## Key findings

- Identification of Stokes curves where oscillations appear
- Conditions for mass ratios that eliminate oscillations
- Validation of asymptotic predictions with numerical simulations

## Abstract

This work presents asymptotic solutions to a singularly-perturbed, period-2 FPUT lattice and uses exponential asymptotics to examine `nanoptera', which are nonlocal solitary waves with constant-amplitude, exponentially small wave trains which appear behind the wave front. Using an exponential asymptotic approach, this work isolates the exponentially small oscillations, and demonstrates that they appear as special curves in the analytically-continued solution, known as `Stokes curves' are crossed. By isolating these the asymptotic form of these oscillations, it is shown that there are special mass ratios which cause the oscillations to vanish, producing localized solitary-wave solutions. The asymptotic predictions are validated through comparison with numerical simulations.