2019/10/27 by Timothy E. Faver, Faver, Timothy E. · 1 citation
Physics and Astronomy · #Analysis of PDEs (math.AP) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #Nonlinear Photonic Systems #Quantum optics and atomic interactions
paper · pdf · doi:10.48550/arxiv.1910.12313
openalex publication_date 2019/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
The mass-in-mass (MiM) lattice consists of an infinite chain of identical\nbeads that are both nonlinearly coupled to their nearest neighbors and linearly\ncoupled to a distinct resonator particle; it serves as a prototypical model of\nwave propagation in granular crystals and metamaterials. We study traveling\nwaves in an MiM lattice whose bead interaction is governed by the cubic\nFermi-Pasta-Ulam-Tsingou potential and whose resonator mass is small compared\nto the bead mass. Excluding a countable number of "antiresonance" resonator\nmasses accumulating at 0, we prove the existence of nanopteron traveling waves\nin this small mass limit. The profiles of these waves consist of the\nsuperposition of an exponentially localized core and a small amplitude periodic\noscillation that itself is a traveling wave profile for the lattice. Our\narguments use functional analytic techniques originally developed by Beale for\na capillary-gravity water wave problem and recently employed in a number of\nrelated nanopteron constructions in diatomic Fermi-Pasta-Ulam-Tsingou lattices.\n