Volume 26, Issue 2, March 2019, Pages 188 - 201
Generalized Solvable Structures and First Integrals for ODEs Admitting an 𝔰𝔩(2, ℝ) Symmetry Algebra
Authors
Paola Morando
DISAA, Università degli Studi di Milano, Via Celoria, 2 Milano, 20133, Italy,paola.morando@unimi.it
Concepción Muriel
Departamento de Matemáticas, Universidad de Cádiz, Puerto Real (Cádiz), 11510, Spain,concepcion.muriel@uca.es
Adrián Ruiz
Departamento de Matemáticas, Universidad de Cádiz, Puerto Real (Cádiz), 11510, Spain,adrian.ruiz@uca.es
Received 11 May 2018, Accepted 24 October 2018, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2019.1591712How to use a DOI?
- Keywords
- Generalized solvable structure; first integral; nonsolvable symmetry algebra
- 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.
- Copyright
- © 2019 The Authors. Published by Atlantis and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
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TY - JOUR AU - Paola Morando AU - Concepción Muriel AU - Adrián Ruiz PY - 2021 DA - 2021/01/06 TI - Generalized Solvable Structures and First Integrals for ODEs Admitting an 𝔰𝔩(2, ℝ) Symmetry Algebra JO - Journal of Nonlinear Mathematical Physics SP - 188 EP - 201 VL - 26 IS - 2 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2019.1591712 DO - 10.1080/14029251.2019.1591712 ID - Morando2021 ER -