第一类阿贝尔方程可积性的初步研究  

Primary Study of Integrability of the First Type Abel Equation

作　　者：刘靖[1] 管克英[1] 

机构地区：[1]北京交通大学理学院,北京100044

出　　处：《北京交通大学学报》2006年第3期104-107,共4页JOURNAL OF BEIJING JIAOTONG UNIVERSITY

摘　　要：根据一般二阶多项式自治系统可积的充要条件,对第一类阿贝尔方程给出了目前已知的几类可积方程的积分因子所具有的特征,并给出了当积分因子限制在其中一类特征时方程系数间的关系,然后进一步证明这类方程可经线性变换化成Bernoulli方程.By means of the sufficient and necessary condition of the general second order polynomial system＇s integrability, in the light of the first type Abel equation, we obtain the characteristics that the integrating factor possesses when the equation is Liouville integrable, and then in one situation, we give the relation among the equation＇s coefficients. Furthermore, we also prove that equations like this must can be transformed into Bernoulli equation through suitable linear transformations.

关 键 词：阿贝尔方程Liouville可积性 广义可积 积分因子 线性变换 

分 类 号：O175.1[理学—数学]