Bright soliton families in the nonlinear Schrödinger equation with a bichromatic linear lattice

We demonstrate that a defocusing cubic nonlinearity with a bichromatic lattice can support various types of bright soliton families, including fundamental solitons and their clusters with an arbitrary number of peaks. We investigate the profiles, powers, amplitudes, stability domains, and propagation dynamics of these soliton families in both the first and second linear Bloch band gaps. Notably, the profiles of soliton families in the bichromatic lattice are different from the counterparts in the monochromatic lattice; specifically, additional humps appear adjacent to the central major peaks of the solitons. This phenomenon becomes more pronounced when the magnitude of the propagation constant becomes large. Introduction of the second lattice makes the gaps significantly wider and offers the possibility of controlling the shape of monochromatic solitons. The stability domains of such solitons are obtained by the method of linear stability analysis and are verified by direct numerical simulations. As the propagation constant increases, instabilities develop in the second band gap and close to the band edge. Curiously, the soliton families under low strengths of bichromatic lattice are always unstable in the second band gap, whereas the ones under high strengths are always stable.