Journal of Nonlinear Mathematical Physics

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Volume 27, Issue 2, January 2020, Pages 185 - 198

The Lie symmetry group of the general Liénard-type equation

Authors
Ágota Figula, Gábor Horváth, Tamás Milkovszki, Zoltán Muzsnay
University of Debrecen, Institute of Mathematics, Pf. 400, Debrecen, 4002, Hungary,figula@science.unideb.hu,ghorvath@science.unideb.hu,milkovszki@science.unideb.hu,muzsnay@science.unideb.hu
Received 8 June 2019, Accepted 13 August 2019, Available Online 27 January 2020.
DOI
10.1080/14029251.2020.1700623How to use a DOI?
Keywords
second order ordinary differential equation; Liénard-type equation; Levinson–Smith-type equation; Lie group; symmetry analysis; Lie algebra of infinitesimal symmetries
Abstract

We consider the general Liénard-type equation u¨=∑k=0nfku˙k for n ≥ 4. This equation naturally admits the Lie symmetry ∂∂t. We completely characterize when this equation admits another Lie symmetry, and give an easily verifiable condition for this on the functions f0,..., fn. Moreover, we give an equivalent characterization of this condition. Similar results have already been obtained previously in the cases n = 1 or n = 2. That is, this paper handles all remaining cases except for n = 3.

Copyright
© 2020 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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Next Article In Issue>
Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
27 - 2
Pages
185 - 198
Publication Date
2020/01/27
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2020.1700623How to use a DOI?
Copyright
© 2020 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/).

Cite this article

risenwbib
TY  - JOUR
AU  - Ágota Figula
AU  - Gábor Horváth
AU  - Tamás Milkovszki
AU  - Zoltán Muzsnay
PY  - 2020
DA  - 2020/01/27
TI  - The Lie symmetry group of the general Liénard-type equation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 185
EP  - 198
VL  - 27
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2020.1700623
DO  - 10.1080/14029251.2020.1700623
ID  - Figula2020
ER  -