Symmetry Solutions of a Third-Order Ordinary Differential Equation which Arises from Prandtl Boundary Layer Equations

It is known that the classification of the Lie algebras is a classical problem. Due to Levi’s Theorem the question can be reduced to the classification of semi-simple and solvable Lie algebras. This paper is devoted to classify the Lie algebra generated by the Lie symmetry group of the Chazy equation. We also present explicitly the one parame-ter subgroup related to the infinitesimal generators of the Chazy symmetry group. Moreover the classification of the Lie algebra associated to the optimal system is investigated. La clasificación de las álgebras de Lie es un problema clásico. Acorde al teorema de Levi la cuestión puede reducirse a la clasificación de álgebras de Lie semi-simples y solubles. Este artículo está dedicado a clasificar el álgebra de Lie generada por el grupo de simetría de Lie para la ecuación de Chazy. También presentamos explícitamente los subgrupos a un parámetro relacionados con los generadores de las simetrías del grupo de Chazy. Además, la clasificación de la álgebra de Lie asociada al sistema optimo es investigada.

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“…The generating operators of Lie symmetry group to (1) are presented in [13] by the following vector fields:…”

Section: Lie Algebra Classification For Chazy's Equationmentioning

confidence: 99%

Lie algebra classification for the Chazy equation and further topics related with this algebra

et al. 2021

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“…In Table 2, two dimensional algebras, invariant equations [17,18,19] and the obtained discrete symmetries are presented. where c is the constant of integration.…”

Section: Two Dimensional Algebramentioning

confidence: 99%

Discrete Symmetry Transformations of Third Order Ordinary Differential Equations and Applications

Bibi

Ферозе

2020

Wseas Transactions on Mathematics

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Third order ordinary differential equations have already been classified by the Lie algebra they admit. Invariant equations corresponding to these Lie algebras are also available in the literature [17]. In this paper, list of all discrete symmetries corresponding to these invariant ordinary differential equations, are obtained. Some particular examples are given to show the significance of the work.

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“…In [17], Ibragimov and Nucci, using the theory of Lie symmetries, were able to reduce (4) by the method of semi-canonical variables. In [1] the theory of non-local Lie symmetries was used to reduce (4), and later in [23] an improvement was presented. In [2], Arrigo calculated the group of symmetries and the invariant transformation of this group using canonical variables.…”

Section: Introductionmentioning

confidence: 99%

Lie group symmetries' complete classification for a generalized Chazy equation and its equivalence group

Acevedo

Duque

Loaiza

2021

RMTA

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Symmetry Solutions of a Third-Order Ordinary Differential Equation which Arises from Prandtl Boundary Layer Equations

Abstract: The similarity solution to Prandtl's boundary layer equations for two-dimensional and radial flows with vanishing or constant mainstream velocity gives rise to a thirdorder ordinary differential equation which depends on a parameter α.

Cited by 16 publications

References 12 publications

Lie algebra classification for the Chazy equation and further topics related with this algebra

Lie algebra classification for the Chazy equation and further topics related with this algebra

Discrete Symmetry Transformations of Third Order Ordinary Differential Equations and Applications

Lie group symmetries' complete classification for a generalized Chazy equation and its equivalence group

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