1987
DOI: 10.1088/0305-4470/20/16/020
|View full text |Cite
|
Sign up to set email alerts
|

A class of second-order differential equations and related first-order systems

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1
1

Citation Types

0
45
0

Year Published

1989
1989
2015
2015

Publication Types

Select...
4
4

Relationship

0
8

Authors

Journals

citations
Cited by 33 publications
(46 citation statements)
references
References 12 publications
0
45
0
Order By: Relevance
“…(10), (11), (13) and (14). It can be directly verified that the first integral of the dynamical system formed by (10) and (11) is given by…”
Section: The De Sitter Model In Scalartensor Cosmologiesmentioning
confidence: 99%
“…(10), (11), (13) and (14). It can be directly verified that the first integral of the dynamical system formed by (10) and (11) is given by…”
Section: The De Sitter Model In Scalartensor Cosmologiesmentioning
confidence: 99%
“…Firstly we are immediately struck by the resemblance to the coefficients in the expansion of a cubic binomial. This suggests the change of variables [7,12,15,31,32] and in particular is known, for certain values of the coefficients, to have eight symmetries instead of the obvious two of invariance under time translation and selfsimilarity, thereby making it linearisable [30].…”
Section: First Reductionmentioning
confidence: 99%
“…In principle one can use these symmetries to obtain the solution, but they are particularly complicated and there is an easier route to the solution. It is known [7] that the equations which belong to this class can be expressed as a simple third order equation by means of a Riccati transformation. We put v = αẇ w , (2.27) where α is a constant to be determined to give the third order equation an optimal simplicity [1].…”
Section: General Solutionmentioning
confidence: 99%
“…The example which we have chosen to illustrate the symmetry methods is the modified Emden equation (MEE) [48,49,50,51,52,53,54,55] …”
Section: Introductionmentioning
confidence: 99%