Nonlinear bandgap transmission with zero frequency in a cross-stitch lattice

Abstract

We consider a model for a cross-stitch lattice with onsite nonlinearity. The linear analysis and the determination of the homoclinic threshold for this model are carried out theoretically. In the case of a self-focusing nonlinearity, we show that the traveling bandgap soliton is possible as a result from the periodic excitation of the edge of the chains. Contrary to the usual supratransmission phenomenon, the generation of traveling solitons is possible by driving the lattice with zero frequency and constant amplitude. In the case of defocusing nonlinearities, the heteroclinic orbit is obtained with the frequency within the phonon band. By exciting one component of complex waves, a traveling phonon kink is obtained. Meanwhile, in the case of the driving of two complex waves with zero phonon and nonzero phonon frequencies, respectively, the fly phonon breather is observed. The collision of the waves from the flat band and phonon band gives the traveling bright carry by the traveling kink. These results are obtained through computer simulations.