Multipole solitons in saturable nonlinear lattices

We demonstrate that both fundamental and multipole soliton families can be generated and stabilized in purely saturable nonlinear lattices, which can be readily realized in nonlinear optics or Bose–Einstein condensates. The waveforms and soliton power of these soliton families, produced in the nonlinear Schrödinger equation, are highly affected by the propagation constant and the strength of nonlinearity. In particular, the amplitude of solitons increases with the increase of the propagation constant, while it decreases with the increase of the strength of nonlinearity. We investigate in detail the stability of such solitons. Beside the perturbed propagation, the stable propagation with modulated parameters that can change during propagation, is also considered, e.g., the one with the modulation of the period of the nonlinear lattice and the other one with the modulation of the strength of saturation. It is verified that the rules of variation for all soliton families are consistent with the ones for modulated parameters.