Volume 16, Issue Supplement 1, December 2009, Pages 137 - 147
Integration of Systems of First-Order Equations Admitting Nonlinear Superposition
Authors
N. H. Ibragimov
Department of Mathematics and Science, Research Centre ALGA: Advances in Lie Group Analysis, Blekinge Institute of Technology, SE-371 79 Karlskrona, Sweden
Received 13 June 2009, Accepted 7 September 2009, Available Online 7 January 2021.
- DOI
- 10.1142/S1402925109000364How to use a DOI?
- Keywords
- Nonlinear superposition; Vessiot–Guldberg–Lie algebras; standard forms of Lie algebras; canonical variables
- Abstract
Systems of two nonlinear ordinary differential equations of the first order admitting nonlinear superpositions are investigated using Lie’s enumeration of groups on the plane. It is shown that the systems associated with two-dimensional Vessiot–Guldberg–Lie algebras can be integrated by quadrature upon introducing Lie’s canonical variables. The knowledge of a symmetry group of a system in question is not needed in this approach. The systems associated with three-dimensional Vessiot–Guldberg–Lie algebras are classified into 13 standard forms 10 of which are integrable by quadratures and three are reduced to Riccati equations.
- Copyright
- © 2009 The Authors. Published by Atlantis Press 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/).
Cite this article
TY - JOUR AU - N. H. Ibragimov PY - 2021 DA - 2021/01/07 TI - Integration of Systems of First-Order Equations Admitting Nonlinear Superposition JO - Journal of Nonlinear Mathematical Physics SP - 137 EP - 147 VL - 16 IS - Supplement 1 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925109000364 DO - 10.1142/S1402925109000364 ID - Ibragimov2021 ER -