Journal of Nonlinear Mathematical Physics

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Volume 8, Issue 2, May 2001, Pages 211 - 216

First Integrals and Parametric Solutions for Equations Integrable Through Lie Symmetries

Authors
C. Géronimi, P.G.L. Leach, M.R. Feix
Corresponding Author
C. Géronimi
Received 10 October 2000, Accepted 3 March 2001, Available Online 1 May 2001.
DOI
10.2991/jnmp.2001.8.2.4How to use a DOI?
Abstract

We present here the explicit parametric solutions of second order differential equations invariant under time translation and rescaling and third order differential equations invariant under time translation and the two homogeneity symmetries. The computtion of first integrals gives in the most general case, the parametric form of the general solution. For some polynomial functions we obtain a time parametrisation quadrature which can be solved in terms of "known" functions.

Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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<Previous Article In Issue
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
8 - 2
Pages
211 - 216
Publication Date
2001/05/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.2001.8.2.4How to use a DOI?
Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - C. Géronimi
AU  - P.G.L. Leach
AU  - M.R. Feix
PY  - 2001
DA  - 2001/05/01
TI  - First Integrals and Parametric Solutions for Equations Integrable Through Lie Symmetries
JO  - Journal of Nonlinear Mathematical Physics
SP  - 211
EP  - 216
VL  - 8
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2001.8.2.4
DO  - 10.2991/jnmp.2001.8.2.4
ID  - Géronimi2001
ER  -