Floquet lattice solitons in zigzag modulated waveguide arrays with zero average modulation: Exponential localization and linear stability

We consider the basic tight-binding model for an array of waveguide arrays with periodic zigzag modulations in the longitudinal direction and local Kerr nonlinearity, focusing on the case with zero average modulation. From the Floquet spectrum of the linearized Su-Schrieffer-Heeger (SSH)-like system, we identify the various gaps where nonlinear solutions may exist, exponentially localized in the bulk and/or at edges. For the fully nonlinear system, numerical continuation yields families of exponentially localized Floquet lattice solitons, calculated to computer precision. Numerical Floquet linear stability analysis shows regimes of stability and explores instability scenarios appearing from internal mode resonances.