关于一类一阶非线性常微分方程解空间的显易结构

On Explicit Structure of Solution Space of a Class of the First Order Nonlinear Ordinary Differential Equation

中文关键词:  解空间  标准可积方程  显易结构

英文关键词:solution space  canonical integrable equation  explicit structure.

中文摘要:

      文章以定理１．１为基础，引入标准可积方程的概念，进而根据已知方程ｗ′＝∑sum from ｉ＝０ to n ａ_ｉ（ｚ）ｗ^ｉ（ｚ）的ｎ＋１个系数，给出了该方程解空间具有显易结构的判别准则．一方面，根据该准则，可以对该类非线性常微分方程解空间结构作出显易结构的判定，从而可以对其解空间进行定性解析分析；另一方面，该准则可以作为判定该类非线性常微分方程在复域上能否变量分离之准则

英文摘要:

      In this paper, the concept of the canonical integrable equation is introduced. A criterion is given involving the n+1 coefficient of a given equation ｗ′＝∑sum from ｉ＝０ to n ａ_ｉ（ｚ）ｗ^ｉ（ｚ） that the solution space of the equation has an explicit structure. According to this criterion, it can be judged that the solution space of this class of nonlinear differential equiation has an explicit or implicit strctrure, therefore, an analytic qualitative analyese can be made on it. Moreover, this criterion can be used to d...