Álgebra óptima y soluciones invariantes para la ecuación de Chazy

Abstract

Se caracterizan las soluciones invariantes para la ecuación de Chazy a partir de los operadores generadores del álgebra óptima, la cual fue obtenida mediante el grupo de simetrías de Lie correspondiente a dicha ecuación.

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

“…The above indicates that the vector space generated by the operators described forms a 3-dimensional Lie algebra. Now, in [12], the Table of commutators for the group of symmetries ( 2) is calculated, see Table 1.…”

“…The solution to this equation implies the solution to the equation , which have applications related to the Prandtl boundary layer for a two-dimensional and radial fluid with uniform main current velocity [11]. The optimal algebra and invariant solutions for the Chazy 2 equation ( 1) is obtained at [12], where the commutators table of the symmetry group of (1) was obtained, which is necessary to the present work too. This paper is devoted to classify the Lie algebra generated by the Lie symmetry group of the Chazy equation and is organized as follows: in section (2) the Lie algebra classification of the Chazy equation is investigated.…”

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

“…Remark 1 In [10], the generators of the symmetry group of Equation ( 4) are presented without showing details for the calculations, these details are presented in [20], where the optimal algebra and new invariant solutions are presented too. Now, the previous results for the generators of the Lie symmetries group coincide with the part (iii) of Proposition 1, after manipulating some constants, which are:…”

“…In [2], Arrigo calculated the group of symmetries and the invariant transformation of this group using canonical variables. Recently, in [20], [22], the authors characterized invariant solutions for the equation ( 4) and Kummer-Schwarz equation, from the generator operators of the optimal system, and using it, they presented new solutions.…”