The Invariant Of Differential Equations And Its Application

In this paper, we will study the nonlinear evolution equations. Using the equiv-alent moving frame theory, we compute the differential invariants, algebraic relations among the differential invariants, invariant solutions of the nonlinear evolution equa-tion. We will study hybrid system, then show an algorithm to calculate the invariants of hybrid system. The main work is as follows:1. Using the equivalent moving frame method to calculate the the invariants and algebraic relations among the differential invariants of CDG equation, coupled KdV-MKdV equations and GCH equation. At the same time, the invariant solutions of GCH equation is obtained.2. We take the advantage of equivalent moving frame method to give an algorithm to calculate the invariants of the hybrid system. And we use the algorithm to compute the invariants of a hybrid system model.