Journal of Nonlinear Mathematical Physics

Volume 9, Issue Supplement 2, September 2002, Pages 1 - 9

Hidden Symmetries, First Integralsvand Reduction of Order of Nonlinear Ordinary Differential Equations

Authors
Barbara Abraham-Shrauner
Corresponding Author
Barbara Abraham-Shrauner
Received 1 February 2002, Available Online 2 September 2002.
DOI
https://doi.org/10.2991/jnmp.2002.9.s2.1How to use a DOI?
Abstract
The reduction of nonlinear ordinary differential equations by a combination of first integrals and Lie group symmetries is investigated. The retention, loss or even gain in symmetries in the integration of a nonlinear ordinary differential equation to a first integral are studied for several examples. The differential equations and first integrals are expressed in terms of the invariants of Lie group symmetries. The first integral is treated as a differential equation where the special case of the first integral equal to zero is examined in addition to the nonzero first integral. The inverse problem for which the first integral is the fundamental quantity enables some predictions of the change in Lie group symmetries when the differential equation is integrated. New types of hidden symmetries are introduced.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
9 - Supplement 2
Pages
1 - 9
Publication Date
2002/09
ISBN
91-631-2869-1
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2002.9.s2.1How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Barbara Abraham-Shrauner
PY  - 2002
DA  - 2002/09
TI  - Hidden Symmetries, First Integralsvand Reduction of Order of Nonlinear Ordinary Differential Equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 1
EP  - 9
VL  - 9
IS  - Supplement 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2002.9.s2.1
DO  - https://doi.org/10.2991/jnmp.2002.9.s2.1
ID  - Abraham-Shrauner2002
ER  -