Using The First Integral Method To Solve A Few Kinds Of Differential Equation’s Wave Solutions

Abstract:Integrable problems of differential equations has been an important element of the differential equation field of study. In general, if the power system is an ordinary differential equation have a sufficient number of the first integral makes all its solutions can be expressed by the first integral function, then it is called integrable. How to construct the first integral of the system to become the key to the question of integrability, the first integral and integrability is an important concept. But unfortunately, the general ordinary differential equation dynamic systems, so far no one to identify effective ways to find the first integral. The article will present two types of ordinary differential equations and two types of nonlinear partial differential equations, and highlights how to use the first integral method to solve these two types of new traveling wave solutions of nonlinear partial differential equations, ie, coupled Burgers-KdV equations, the Fitzhugh-Nagumo equations. The results and development of existing work, the wide range of effectiveness of this method has been confirmed.