Adrián Ruiz, Concepción Muriel, “Solvable Structures Associated to the Nonsolvable Symmetry Algebra <nobr>$\mathfrak{sl}(2,\mathbb{R})$</nobr>”, SIGMA, 2016, Volume 12,077, 18 pp.

This article is cited 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.

MSC: 34A05; 34A26; 34C14

Received: November 11, 2015; in final form August 3, 2016; Published online August 8, 2016

Language: English

DOI: 10.3842/SIGMA.2016.077