Some New Approaches to Duffing Equation with Strongly and High Order Nonlinearity （Ⅱ） Parametrized Perturbation Technique  

作　　者：JihuanHE 

机构地区：ShanghaiInstituteofAppliedMathematicsandMechanics,ShanghaiUniversity,Shanghai200072,China

出　　处：《Communications in Nonlinear Science and Numerical Simulation》1999年第1期81-83,共3页非线性科学与数值模拟通讯（英文版）

摘　　要：For the strongly nonlinear equations without small parameter,a transformation u=βv can be introduced for the nonlinear equation L(u)+N(u)=0,where L and N are general linear and nonlinear differential operators respectively,β is sufficiently small.Therefore,a strongly non-linear system is transformed into a small parameter system with respect to the new introduced parameter β,thus various traditional perturebation techniques can be applied.By lindstedt-Poincare method,a perturbation solution for DUffing equation with 5th order nonlinearity is obtained,which is valid not only for the small parameter ε in the equation,but also for very large values of ε.

关 键 词：非线性微分方程 高阶DUFFING方程 参数化微扰技术 

分 类 号：O175.14[理学—数学]