Traveling waves in chains of pendula

The existence of traveling wave solutions for the discrete, forced, damped sine-Gordon equation, which serves as a model of arrays of Josephson junctions and coupled pendula, in the case of small coupling coefficient has been addressed before. In this paper we prove the existence of a discrete traveling wave in a lattice of coupled pendula with a large coupling coefficient in the presence of damping and forcing, and show the global stability of this wave.

► We prove the existence of a traveling wave in lattices of coupled pendula.
► We show that the traveling wave is a global attractor.
► The wave that we find is born in a saddle–node bifurcation.