  The diatomic Fermi-Pasta-Ulam-Tsingou (FPUT) lattice is an infinite chain of
alternating particles connected by identical nonlinear springs. We prove the
existence of micropteron traveling waves in the diatomic FPUT lattice in the
limit as the ratio of the two alternating masses approaches 1, at which point
the diatomic lattice reduces to the well-understood monatomic FPUT lattice.
These are traveling waves whose profiles asymptote to a small periodic
oscillation at infinity, instead of vanishing like the classical solitary wave.
We produce these micropteron waves using a functional analytic method,
originally due to Beale, that was successfully deployed in the related long
wave and small mass diatomic problems. Unlike the long wave and small mass
problems, this equal mass problem is not singularly perturbed, and so the
amplitude of the micropteron's oscillation is not necessarily small beyond all
orders (i.e., the traveling wave that we find is not necessarily a nanopteron).
The central challenge of this equal mass problem hinges on a hidden solvability
condition in the traveling wave equations, which manifests itself in the
existence and fine properties of asymptotically sinusoidal solutions (Jost
solutions) to an auxiliary advance-delay differential equation.
