On generalized Sundman transformation method, first integrals, symmetries and solutions of equations of Painleve-Gambier type

被引：10

作者：

Guha, Partha ^{[1
,2
]}

Khanra, Barun ^{[3
]}

Choudhury, A. Ghose ^{[4
]}

机构：

[1] Max Planck Inst Math Sci, D-04103 Leipzig, Germany

[2] SN Bose Natl Ctr Basic Sci, Kolkata 700098, India

[3] Sailendra Sircar Vidyalaya, Kolkata 700004, India

[4] Surendranath Coll, Dept Phys, Kolkata 700009, W Bengal, India

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 72卷 / 7-8期

关键词：

Sundman transformation; Sundman symmetries; Painleve-Gambier equations; First integrals; Jacobi equation; ORDINARY DIFFERENTIAL-EQUATIONS; 2ND-ORDER;

D O I：

10.1016/j.na.2009.12.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We employ the generalized Sundman transformation method to obtain certain new first integrals of autonomous second-order ordinary differential equations belonging to the Painleve-Gambier classification scheme. This method not only yields systematically the known first integrals of a large number of the Painleve-Cambier equations but also some time dependent ones, which greatly simplify the computation of their corresponding solution. In addition we also compute the Sundman symmetries of these equations. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：3247 / 3257

页数：11

共 18 条

[1] [Anonymous], 1896, Determination des invariants ponctuels de l'equation differentielle ordinaire du second ordre
[2] [Anonymous], 1900, Bull. Soc. Math. Fr
[3] [Anonymous], ANAL SOLUTIONS PAINL
[4] Bluman G.W., 1996, Symmetries and Differential Equations.
[5] CHANDRASEKAR VK, ARXIVNLIN0510036V1
[6] LINEARIZATION UNDER NONPOINT TRANSFORMATIONS
DUARTE, LGS
MOREIRA, IC
SANTOS, FC
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1994, 27 (19): : L739 - L743
[7] Transformation between a generalized Emden-Fowler equation and the first Painleve transcendent
Euler, Marianna
Euler, Norbert
Stromberg, Anders
Astrom, Erik
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2007, 30 (16) : 2121 - 2124
[8] Sundman symmetries of nonlinear second-order and third-order ordinary differential equations
Euler, N
Euler, M
[J]. JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2004, 11 (03) : 399 - 421
[9] Linearisable third-order ordinary differential equations and generalised Sundman transformations:: The case X′"=0
Euler, N
Wolf, T
Leach, PGL
Euler, M
[J]. ACTA APPLICANDAE MATHEMATICAE, 2003, 76 (01) : 89 - 115
[10] GAMBIER B., 1910, Acta Math., V33, P1, DOI [10.1007/BF02393211, DOI 10.1007/BF02393211)]

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