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The diatomic Fermi-Pasta-Ulam-Tsingou (FPUT) lattice is an infinite chain ofalternating particles connected by identical nonlinear springs. We prove theexistence of micropteron traveling waves in the diatomic FPUT lattice in thelimit as the ratio of the two alternating masses approaches 1, at which pointthe diatomic lattice reduces to the well-understood monatomic FPUT lattice.These are traveling waves whose profiles asymptote to a small periodicoscillation 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 longwave and small mass diatomic problems. Unlike the long wave and small massproblems, this equal mass problem is not singularly perturbed, and so theamplitude of the micropteron's oscillation is not necessarily small beyond allorders (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 solvabilitycondition in the traveling wave equations, which manifests itself in theexistence and fine properties of asymptotically sinusoidal solutions (Jostsolutions) to an auxiliary advance-delay differential equation.

Micropteron traveling waves in diatomic Fermi-Pasta-Ulam-Tsingou lattices under the equal mass limit