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

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.

24 pages, 8 figures, 1 table

References in corpus (7)

• Highly Nonlinear Wave Propagation in Elastic Woodpile Periodic Structures
• Wave Propagation in a Strongly Nonlinear Locally Resonant Granular Crystal
• Nanopteron solutions of diatomic Fermi-Pasta-Ulam-Tsingou lattices with small mass-ratio
• Traveling Waves and their Tails in Locally Resonant Granular Systems
• Nanoptera in a Period-2 Toda Chain
• Standing lattice solitons in the discrete NLS equation with saturation
• Globally exact asymptotics for integrals with arbitrary order saddles