Nanoptera and Stokes curves in the 2-periodic Fermi–Pasta–Ulam–Tsingou equation

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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 studying the asymptotic form of these isolated 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.

Original languageEnglish
Article number132239
Pages (from-to)1-13
Number of pages13
JournalPhysica D: Nonlinear Phenomena
Volume402
DOIs
Publication statusPublished - 15 Jan 2020

Keywords

  • Solitary waves
  • Exponential asymptotics
  • Nanoptera
  • FPUT lattice

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