Gap soliton dynamics in an optical lattice as a parametrically driven pendulum

A long wavelength optical lattice is generated in a two-level medium by low-frequency contrapropagating beams. Then a short wave length gap soliton generated by evanescent boundary instability (supratransmission) undergoes a dynamics shown to obey the Newton equation of the parametrically driven pendulum, hence presenting extremely rich, possibly chaotic, dynamical behavior. The theory is sustained by numerical simulations and provides an efficient tool to study soliton trajectories.