The notion of solvable structure is generalized in order to exploit the presence of an sl(2,R) algebra of symmetries for a kth-order ordinary differential equation E with k > 3. In this setting, the knowledge of a generalized solvable structure for E allows us to reduce E to a family of second-order linear ordinary differential equations depending on k − 3 parameters. Examples of explicit integration of fourth and fifth order equations are provided in order to illustrate the procedure.

Generalized Solvable Structures and First Integrals for ODEs Admitting an sl(2,R) Symmetry Algebra / P. Morando, C. Muriel, A. Ruiz. - In: JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS. - ISSN 1402-9251. - 26:2(2019), pp. 188-201. [10.1080/14029251.2019.1591712]

Generalized Solvable Structures and First Integrals for ODEs Admitting an sl(2,R) Symmetry Algebra

P. Morando
;
2019

Abstract

The notion of solvable structure is generalized in order to exploit the presence of an sl(2,R) algebra of symmetries for a kth-order ordinary differential equation E with k > 3. In this setting, the knowledge of a generalized solvable structure for E allows us to reduce E to a family of second-order linear ordinary differential equations depending on k − 3 parameters. Examples of explicit integration of fourth and fifth order equations are provided in order to illustrate the procedure.
first integral; Generalized solvable structure; nonsolvable symmetry algebra
Settore MAT/07 - Fisica Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/636580
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