INVERSE OPERATOR METHOD FOR SOLUTIONS OF NONLINEAR DYNAMICAL EQUATIONS AND SOME TYPICAL APPLICATIONS
逆算符方法求解非线性动力学方程及其一些应用实例

In this paper, the inverse operator method (IOM) is described briefly. We have realized the IOM for the solutions of nonlinear dynamical equations by the mathematics-mechanization (MM) with computers. They can then offer a new and powerful method applicable to many areas of physics. We have applied them successfully to study the chaotic behaviors of some nonlinear dynamical equations. As typical examples, the well-known Lorentz equation, generalized Duffing equation and two coulped generalized Duffing equations are investigated by the use of the IOM and the MM. The results are in good agreement with those given by Runge-Kutta method. So the IOM realized by the MM is of potential application valuable in nonlinear physics and many other fields.