The mass-in-mass (MiM) lattice consists of an infinite chain of identical beads that are both nonlinearly coupled to their nearest neighbors and linearly coupled to a distinct resonator particle; it serves as a prototypical model of wave propagation in granular crystals and metamaterials. We study traveling waves in an MiM lattice whose bead interaction is governed by the cubic Fermi–Pasta–Ulam–Tsingou potential and whose resonator mass is small compared to the bead mass. Excluding a countable number of “antiresonance” resonator masses accumulating at 0, we prove the existence of nanopteron traveling waves in this small mass limit. The profiles of these waves consist of the superposition of an exponentially localized core and a small amplitude periodic oscillation that itself is a traveling wave profile for the lattice. Our arguments use functional analytic techniques originally developed by Beale for a capillary–gravity water wave problem and recently employed in a number of related nanopteron constructions in diatomic Fermi–Pasta–Ulam–Tsingou lattices.

质量块（MiM）晶格由无数个相同的磁珠链组成，这些磁珠既非线性耦合到它们的最近邻居，又线性耦合到一个不同的谐振器粒子。它用作颗粒晶体和超材料中波传播的原型模型。我们研究MiM晶格中的行波，该行的磁珠相互作用受立方费米-帕斯塔-乌拉姆-津古势的控制，并且其谐振器质量比磁珠质量小。排除可计数的“反共振”谐振器质量累积为0的数量，我们证明了在这个小的质量极限中存在纳米级行波。这些波的轮廓由指数局部磁心和小幅度周期性振荡的叠加组成，其本身就是晶格的行进波轮廓。