Lie point symmetries, partial Noether operators and first integrals of the Painlev¨¦¨CGambier equations

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• 作者：A.G. Johnpillai^a ;   ; ^{andrewgratienj@yahoo.com} ; C.M. Khalique^a ;   ; ^{Masood.Khalique@nwu.ac.za} ; F.M. Mahomed^b ;   ; ^{Fazal.Mahomed@wits.ac.za}
• 关键词：Lie linearization ; Partial Lagrangian ; Partial Noether operators ; First integrals ; Jacobi equation ; Painlevé ; &ndash ; Gambier equations
• 刊名：Nonlinear Analysis
• 出版年：2012
• 出版时间：January 2012
• 年：2012
• 卷：75
• 期：1
• 页码：30-36
• 全文大小：209 K

文摘

We utilize the Lie¨CTress¨¦ linearization method to obtain linearizing point transformations of certain autonomous nonlinear second-order ordinary differential equations contained in the Painlev¨¦¨CGambier classification. These point transformations are constructed using the Lie point symmetry generators admitted by the underlying Painlev¨¦¨CGambier equations. It is also shown that those Painlev¨¦¨CGambier equations which have a few Lie point symmetries and hence are not linearizable by this method can be integrated by a quadrature. Moreover, by making use of the partial Lagrangian approach we obtain time dependent and time independent first integrals for these Painlev¨¦¨CGambier equations which have not been reported in the earlier literature. A comparison of the results obtained in this paper is made with the ones obtained using the generalized Sundman linearization method.