Small-amplitude periodic travelling waves in dimer Fermi–Pasta–Ulam–Tsingou lattices without symmetry

Abstract We prove the existence of small-amplitude periodic travelling waves in dimer Fermi–Pasta–Ulam–Tsingou (FPUT) lattices without assumptions of physical symmetry. Such lattices are infinite, one-dimensional chains of coupled particles in which the particle masses and/or the potentials of the coupling springs can alternate. Previously, periodic travelling waves were constructed in a variety of limiting regimes for the symmetric mass and spring dimers, in which only one kind of material data alternates. The new results discussed here remove the symmetry assumptions by exploiting the gradient structure and translation invariance of the travelling wave problem. Together, these features eliminate certain solvability conditions that symmetry would otherwise manage and facilitate a bifurcation argument involving a two-dimensional kernel and cokernel.