On solutions of third and fourth-order time dependent Riccati equations and the generalized Chazy system

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• 作者：Partha Guha^a ; ^{partha@bose.res.in} ; A. Ghose Choudhury^b ; ^{a_ghosechoudhury@rediffmail.com} ; Barun Khanra^c ; ^{barunkhanra@rediffmail.com}
• 关键词：Nonlocal transformation ; First integrals ; Third and fourth-order Riccati equation ; Generalized Chazy equation ; F-XVI Bureau symbol PI
• 刊名：Communications in Nonlinear Science and Numerical Simulation
• 出版年：2012
• 期刊代码：89_10075704
• 类别：ph
• 出版时间：November, 2012
• 卷：17
• 期：11
• 页码：4053-4063
• 文件大小：263 K

摘要

We introduce a new transformation (nonlocal) to find the general solutions of some equations belonging to the third and fourth-order time dependent Riccati class of equations. These are in turn related to the Chazy polynomial class and the time dependent F-XVI Bureau symbol PI equations respectively.