Abstract: We considered a nonlinear disturbed model for a class of singular perturbation trajectories of Fermi gases optical lattices. Firstly, the degenerate solution of the trajectories of the Fermi gases optical lattices model was given. Secondly, the outer solution of the system was given by using the singular perturbation method, and the layer type corrective term of the system was given by using a stretch variable methods. Finally, the arbitrary order asymptotic solution of the trajectory of nonlinear disturbed model for singular perturbation Fermi gases optical lattices and the uniformly valid asymptotic expansions of solution were given.

Key words: disturbance, trajectory, Fermi gas