Abstract: Applying the perturbation method, the nonlinear evolution equations are expanded as multi-order approximate equations. And based on Lam equation and Lam function, these multi-order approximate equations can be solved by Jacobi elliptic function expansion method, where multi-order exact solutions of nonlinear evol ution equations are derived. Then the invariants of the multi-order exact soluti ons are found among different nonlinear evolution equations.

Keywords: 
• Lam function /
• Jacobi elliptic function /
• multi-order exact solution /
• nonlinear evolution equation /
• perturbation method /
• invariants