Lustri, Christopher J. Nanoptera and Stokes curves in the 2-periodic Fermi-Pasta-Ulam-Tsingou equation. (English) Zbl 1453.82045 Physica D 402, Article ID 132239, 13 p. (2020). Summary: 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. Cited in 10 Documents MSC: 82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems 34A33 Ordinary lattice differential equations Keywords:solitary waves; exponential asymptotics; nanoptera; Fermi-Pasta-Ulam-Tsingou lattice Software:DLMF PDFBibTeX XMLCite \textit{C. J. Lustri}, Physica D 402, Article ID 132239, 13 p. (2020; Zbl 1453.82045) Full Text: DOI arXiv References: [1] Friesecke, G.; Pego, R. L., Solitary waves on FPU lattices: I. Qualitative properties, renormalization and continuum limit, Nonlinearity, 12, 6, 1601 (1999) · Zbl 0962.82015 [2] Friesecke, G.; Pego, R. L., Solitary waves on FPU lattices: II. Linear implies nonlinear stability, Nonlinearity, 15, 4, 1343 (2002) · Zbl 1102.37311 [3] Friesecke, G.; Wattis, J. A.D., Existence theorem for solitary waves on lattices, Comm. Math. 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