Concepción Muriel | Searcharxiv

arXiv2016

Solvable Structures Associated to the Nonsolvable Symmetry Algebra $\mathfrak{sl}(2,\mathbb{R})$

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.

math.CA↗

arXiv2012

Nonlocal Symmetries, Telescopic Vector Fields and $λ$-Symmetries of Ordinary Differential Equations

This paper studies relationships between the order reductions of ordinary differential equations derived by the existence of $λ$-symmetries, telescopic vector fields and some nonlocal symmetries obtained by embedding the equation in an auxiliary system. The results let us connect such nonlocal symmetries with approaches that had been previously introduced: the exponential vector fields and the $λ$-coverings method. The $λ$-symmetry approach let us characterize the nonlocal symmetries that are useful to reduce the order and provides an alternative method of computation that involves less unknowns. The notion of equivalent $λ$-symmetries is used to decide whether or not reductions associated to two nonlocal symmetries are strictly different.

math.CA↗