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This article is cited in 11 scientific papers (total in 11 papers)
Solvable Structures Associated to the Nonsolvable Symmetry Algebra $\mathfrak{sl}(2,\mathbb{R})$
Adrián Ruiz, Concepción Muriel Department of Mathematics, University of Cádiz, 11510 Puerto Real, Spain
Abstract:
Third-order ordinary differential equations with Lie symmetry algebras isomorphic to the nonsolvable algebra $\mathfrak{sl}(2,\mathbb{R})$ admit solvable structures. These solvable structures can be constructed by using the basis elements of these algebras. Once the solvable structures are known, the given equation can be integrated by quadratures as in the case of solvable symmetry algebras.
Keywords:
first integral; solvable structure; $\mathcal{C}^{\infty}$-symmetry; nonsolvable algebra.
Received: November 11, 2015; in final form August 3, 2016; Published online August 8, 2016
Citation:
Adrián Ruiz, Concepción Muriel, “Solvable Structures Associated to the Nonsolvable Symmetry Algebra $\mathfrak{sl}(2,\mathbb{R})$”, SIGMA, 12 (2016), 077, 18 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1159 https://www.mathnet.ru/eng/sigma/v12/p77
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