基于Mathematica的特殊阿贝尔方程的可积性及其判定  

Integrability Determination of Special Abelian Equation with Mathematica Software

作　　者：周大勇[1] 

机构地区：[1]大连交通大学数理系,辽宁大连116028

出　　处：《大连铁道学院学报》2005年第2期6-9,共4页Journal of Dalian Railway Institute

摘　　要：对形如y'=f3(x)y3+f2(x)y2+f1(x)y的特殊阿贝尔方程的精确解,一般是不能通过对方程的系数进行有限次的代数运算及有限次的微积分运算求得的.利用变换群的思想,通过具体的分式线性变换,给出了一种新的积分方法,得到了两组新的判定上述特殊阿贝尔方程可积的充分条件,利用数学软件mathematica,实现了计算机对该类方程可积性的自动判定与精确求解.Commonly,the exact solution to the special Abelian equation： y^1 =f3（x）y^3 ＋f2（x）y＆2 ＋ f1 （x） y can not be obtained by limit algebric operation and equation coefficient calculation. By transformation group,a new integrable method is devoloped, and two conditions to the special Abelian equation is acquired by accurate linear fractional transformation. Thus, automatic determination is realized and the accurate solution can be reached by Mathematica software.

关 键 词：阿贝尔方程 分式线性变换 可积性 

分 类 号：O175.1[理学—数学]