Solitary waves in diatomic chains

We consider the mechanism of formation of isolated localized wave structures in the diatomic Fermi-Pasta-Ulam (FPU) model. Using a singular multiscale asymptotic analysis in the limit of high mass mismatch between the alternating elements, we obtain the typical slow-fast time scale separation and formulate the Fredholm orthogonality condition approximating a sequence of mass ratios supporting the formation of solitary waves in the general type of diatomic FPU models. This condition is made explicit in the case of a diatomic Toda lattice. Results of numerical integration of the full diatomic Toda lattice equations confirm the formation of these genuinely localized wave structures at special values of the mass ratio that are close to the analytical predictions when the ratio is sufficiently small.