The New Multi-Order Exact Solutions of Some Nonlinear Evolution Equations

Abstract

Based on the Lamé equation and Jacobi elliptic function, the perturbation method is applied to some nonlinear evolution equations. And there many multi-order solutions are derived to these nonlinear evolution equations. These multi-order solutions correspond to the different periodic solutions, which can degenerate to the different soliton solutions. The method can be also applied to many other nonlinear evolution equations.