一类弱非线性摄动方程的渐近解  

The asymptotic solution of a class of weakly nonlinear perturbation equations

作　　者：施春菁[1] 欧阳成[1] 

机构地区：[1]湖州师范学院数学系,浙江湖州313000

出　　处：《华中师范大学学报（自然科学版）》2013年第1期12-15,共4页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金项目(11071205;10902076);浙江省自然科学基金项目(Y6110502);浙江省普通高校省组精品课程<常微分方程>建设项目

摘　　要：研究了一类一般的弱非线性摄动方程,将方程的非齐次项表示为Fourier级数,在3种情况下分别用直接展开法、重正规化方法、多重尺度法得到了一致有效的渐近解,并将其运用于相关参考文献中特殊的弱非线性摄动方程,具体且精确地用Fourier系数给出了解的表达式.在前两种情况下,得到了与其一致的结果,用较高的观点揭示了解的本质;还针对参考文献中未讨论的第3种情况,得到了一阶渐近解.A class of general weakly nonlinear perturbation equations is studied.The nonhomogeneous term of the equation is expressed as Fourier series.The uniformly valid asymptotic solutions are obtained using the direct expansion method,the re-normalization method,the multiple scale method,respectively for three different cases.The expression of the solution of a special weakly nonlinear perturbation equation in the related reference is given concretely and exactly by the result with the Fourier coefficients.For the first two cases,the results are consistent with the those in the reference,and the nature of the solution is revealed with a higher point of view.For the third case,the asymptotic solution with first-order is obtained,which was not discussed in the references.

关 键 词：弱非线性 摄动方程 直接展开法 重正规化方法 多重尺度法 

分 类 号：O175.14[理学—数学]