Adomian Approximate Analytic Solutions Of Several Nonlinear Equations

Because of the series form of solutions obtained by the Adomian decomposition method is convergence quickly and easy to calculate, thefore the Adomian decomposition method is widely used to solve linear and nonlinear differential equations since 1980's.The principles of the methods are: firstly, the solved nonlinear equations are divided into several parts; secondly, the solutions of the equations are resolved into infinite components; thirdly, the particular polynomials, which are equivalent to nonlinear parts of the equations, are created; and finally, the components are gradually calculated from low order to high order. So the approximation solutions or exact solutions are obtained.In the paper, generalized 5th order KdV equation, 2N+1 order KdV equation, variable coefficients MKdV and KdV equations are solved using the Adomian decomposition methods, and the approximation solutions are obtained. As well as these solutions are tested using concrete values. The results show that the Adomain decomposition method is more suitable for solving variable coefficient nonlinear equations. It is also shows that the approximate solutions obtained by the method are cannot change basic form of the original equations. So the method has more significance in practically.