All Meromorphic Solutions of Some Algebraic Differential Equations  

作　　者：Wenjun Yuan Zifeng Huang Jinchun Lai Jianming Qi 

机构地区：[1]School of Mathematics and Information Science, Guangzhou University [2]Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University [3]Department of Mathematics and Physics, Shanghai Dianji University

出　　处：《Analysis in Theory and Applications》2014年第1期90-107,共18页分析理论与应用（英文刊）

基　　金：supported by the Visiting Scholar Program of Chern Institute of Mathematics at Nankai University;the support with the NSF of China (No. 11271090, 11326083);NSF of Guangdong Province (S2012010010121);Shanghai university young teacher training program (ZZSDJ12020);projects 10XKJ01, 12C401 and 12C104 from the Leading Academic Discipline Project of Shanghai Dianji University

摘　　要：In this article, we introduce some results with respect to the integrality and exact solutions of some 2nd order algebraic DEs. We obtain the sufficient and necessary conditions of integrable and the general meromorphic solutions of these equations by the complex method, which improves the corresponding results obtained by many authors. Our results show that the complex method provides a powerful mathematical tool for solving a large number of nonlinear partial differential equations in mathematical physics.In this article, we introduce some results with respect to the integrality and exact solutions of some 2nd order algebraic DEs. We obtain the sufficient and necessary conditions of integrable and the general meromorphic solutions of these equations by the complex method, which improves the corresponding results obtained by many authors. Our results show that the complex method provides a powerful mathematical tool for solving a large number of nonlinear partial differential equations in mathematical physics.

关 键 词：Differential equation general solution meromorphic function elliptic function. 

分 类 号：O174.52[理学—数学] O175.29[理学—基础数学]