作　　者： ; ; ; (陈洋洋）;

机构地区： 教育部

出　　处： 《应用数学和力学》 2012年第9期1064-1077,共14页

摘　　要： 提出广义的双曲函数摄动法,用于求解强非线性自治振子的同宿解,克服一般摄动步骤中派生方程须存在显式精确同宿解的限制.以广义双曲函数作为摄动步骤的基本函数,拓展了基于双曲函数的摄动法的适用范围.对同时含2,3次和含4次强非线性项的系统进行求解分析,验证了方法的有效性和精度. A generalized hyperbolic perturbation method was presented for homoclinic solutions of strongly nonlinear autonomous oscillators,in which the perturbation procedure was improved for those systems whose exact homoclinic generating solutions could not be explicitly derived.The generalized hyperbolic functions were employed as the basis functions in the present procedure to extend the validity of the hyperbolic perturbation method.Several strongly nonlinear oscillators with quadratic,cubic and quartic nonlinearity were studied in details to illustrate the efficiency and accuracy of the present method.

关 键 词： 广义双曲函数摄动法 自激系统 同宿解

领　　域： [理学] [理学]