Based on the Lamé equation and Lamé functions, the perturbation method and Jacobi elliptic function expansion method are applied to construct the multi-order exact solutions to the cubic nonlinear Schr?dinger equation. Some new multi-order envelope periodic solutions are found among the nonlinear evolution equations. These multi-order envelope periodic solutions correspond to different periodic solutions, which can degenerate into the different envelope solitary solutions. It is shown that some multi-order asymptotic periodic solutions to some nonlinear evolution equations in term of Jacobi elliptic functions and Lamé equation are explicitly obtained with the aid of symbolic computation.