Asymptotic Solution Of Nonlinear Partial Differential Equations Control The Power System

The investigation of nonlinear oscillation is very important for the nonlinear science. Many methods have been advanced to study weakly nonlinear system, including multiple scale method, KBM method, averaging method, and so on. In recent years, there are increasing interests to study strongly nonlinear system. Compared to linear item, the nonlinear item is not small in these systems. So the traditional perturbation methods may not be applied in strongly nonlinear system directly. Recently, there are some methods are utilized to study it, such as the modified Lindstedt-Poincare method, frequency-incremental method, stroboscopic method etc. More and more, scientists pay attention to it, As the study of solving partial differential equation is very important for the development of mechanics. At present, the primary method to solve it is Galerkin method, which change partial differential equation into ordinary differential equation, and then solve it with the traditional method. In this paper, An asymptotic method have been studied to solve the nonlinear partial difference. The content of nonlinear theory has been enriched. Some methods, which are used to solve strongly nonlinear equation, have been expanded. These studies make abundance in the nonlinear theory and expand the applying range of some method solving strongly nonlinear difference equation. In the first chapter, the actuality of the nonlinear dynamics and the foreground of it have been introduced as well as the main task and the new innovation of the dissertation. In the second chapter, the traveling wave solution of Klein-Gordon equation has been obtained at first, then the asymptotic solution of Klein-Gordon equation with initial condition has been acquired, at last a kind of Klein-Gordon equation's stability has been discussed. In the third chapter, we discussed the problem about partial differential equation with small parameter on the high-order item. In the fourth chapter, the oscillation of a nonlinear beam under the axial harmonic force and the bifurcation of the weak or strongly nonlinear system have been studied.