La géométrie de l'équation y‴=f(x,y,y′,y″)

Neut, Sylvain; Petitot, Michel

doi:10.1016/s1631-073x(02)02507-4

Cited by 47 publications

(62 citation statements)

References 4 publications

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“…Linearization for such equations via other than point transformations has been investigated by many authors (see, e.g. [59,[82][83][84]). Algebra bounds for systems were considered by González-Gascón and González-Lopéz [14].…”

Section: Discussionmentioning

confidence: 99%

Symmetry group classification of ordinary differential equations: Survey of some results

Mahomed

2007

Math Methods in App Sciences

112

110

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SUMMARYAfter the initial seminal works of Sophus Lie on ordinary differential equations, several important results on point symmetry group analysis of ordinary differential equations have been obtained. In this review, we present the salient features of point symmetry group classification of scalar ordinary differential equations: linear nth-order, second-order equations as well as related results. The main focus here is the contributions of Peter Leach, in this area, in whose honour this paper is written on the occasion of his 65th birthday celebrations.

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Section: Discussionmentioning

confidence: 99%

Symmetry group classification of ordinary differential equations: Survey of some results

Mahomed

2007

Math Methods in App Sciences

112

110

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“…A complete analysis and a method to find solutions of the remaining classes would be very important. Again, the higher order equations can be linearized by using the Lie procedure as done by Ibragimov and Meleshko [11] or by the procedure of Neut and Petitot [10]. To what extent is there an overlap between the two procedures?…”

Section: Resultsmentioning

confidence: 99%

“…In particular, there are only three classes possible for the third order ODEs linearizable by point transformations [5], y (x) = 0, y (x) = y(x) and y (x) = α(x)y(x). Two were provided by Chern [6,7] and the third by Neut and Petitot [10], and later by Ibragimov and Meleshko [11]. How can there then be another class?…”

Section: Higher Order Systemsmentioning

confidence: 99%

Geometric Linearization of Ordinary Differential Equations

Qadir¹

2007

SIGMA

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Abstract. The linearizability of differential equations was first considered by Lie for scalar second order semi-linear ordinary differential equations. Since then there has been considerable work done on the algebraic classification of linearizable equations and even on systems of equations. However, little has been done in the way of providing explicit criteria to determine their linearizability. Using the connection between isometries and symmetries of the system of geodesic equations criteria were established for second order quadratically and cubically semi-linear equations and for systems of equations. The connection was proved for maximally symmetric spaces and a conjecture was put forward for other cases. Here the criteria are briefly reviewed and the conjecture is proved.

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“…It was algebraically shown [14] that there are three classes of third-order ODES that are linearizable by point transformations. Subsequently Neut and Petitot [21] and later Ibragimov and Meleshko [9], who used the original Lie procedure [12], determined practical invariant criteria for linearizability of third-order ODEs. Linearization can also be achieved by transformations that are other than point [5].…”

Section: Introductionmentioning

confidence: 99%

Conditional Linearizability of Fourth-Order Semi-Linear Ordinary Differential Equations

Mahomed¹,

Qadir²

2021

JNMP

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By the use of geometric methods for linearizing systems of second-order cubically semi-linear ordinary differential equations and the conditional linearizability of third-order quintically semi-linear ordinary differential equations, we extend to the fourth-order by differentiating the third-order conditionally linearizable equation. This yields criteria for conditional linearizability of a class of fourth-order semi-linear ordinary differential equations, which have not been discussed in the literature previously.

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La géométrie de l'équation y‴=f(x,y,y′,y″)

Cited by 47 publications

References 4 publications

Symmetry group classification of ordinary differential equations: Survey of some results

Symmetry group classification of ordinary differential equations: Survey of some results

Geometric Linearization of Ordinary Differential Equations

Conditional Linearizability of Fourth-Order Semi-Linear Ordinary Differential Equations

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