Existence of generalized solitary waves for a diatomic Fermi-Pasta-Ulam-Tsingou lattice

The paper proves existence of front traveling-wave (generalized solitary-wave) solutions in the diatomic FPUT lattice with explicit leading tanh core, an optical tail of prescribed algebraically small amplitude I=ε^4 I0, and sharp bounds on the localized and periodic corrections. The candidate solution reproduces the theorem’s statement and follows the same Beale-type gluing strategy on a center(-manifold/normal-form) reduction: kink + cut-off periodic tail + small correction, with solvability conditions fixing the phase and frequency shift. Minor discrepancies include the model’s claim of a 4D reduced normal form (the paper’s normal form is effectively 5D by translation invariance) and a few notational scalings in the dispersion determinant. Otherwise the constants, asymptotics, tail structure, and estimates match the paper’s result and method.