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

DOI

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.

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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TY  - JOUR
AU  - Barbara Abraham-Shrauner
PY  - 2002
DA  - 2002/09/02
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  - 10.2991/jnmp.2002.9.s2.1
ID  - Abraham-Shrauner2002
ER  -