Exact solutions and Riccati-type first integrals
- 10.1080/14029251.2017.1418055How to use a DOI?
- λ-symmetry; Sundman transformation; Riccati-type first integral
The λ-symmetry approach is applied to a family of second-order ODEs whose algebra of Lie point symmetries is insufficient to integrate them. The general solution and two functionally independent first integrals of a subclass of the studied equations can be expressed in terms of a fundamental set of solutions of a related second-order linear ordinary differential equation. Remarkably, no equation in the family passes the Lie’s test of linearisation, although all of them can be linearised by generalised Sundman transformations. Several examples, including equations lacking Lie point symmetries, illustrate the presented procedure.
- © 2017 The Authors. Published by Atlantis Press and Taylor & Francis
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- 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 - J. Mendoza AU - C. Muriel PY - 2021 DA - 2021/01/06 TI - Exact solutions and Riccati-type first integrals JO - Journal of Nonlinear Mathematical Physics SP - 75 EP - 89 VL - 24 IS - Supplement 1 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2017.1418055 DO - 10.1080/14029251.2017.1418055 ID - Mendoza2021 ER -