Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2005-11-25
SIGMA 1 (2005), 018, 15 pages
Nonlinear Sciences
Exactly Solvable and Integrable Systems
Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
Scientific paper
10.3842/SIGMA.2005.018
We investigate the symmetry properties of a pair of Ermakov equations. The system is superintegrable and yet possesses only three Lie point symmetries with the algebra sl(2,R). The number of point symmetries is insufficient and the algebra unsuitable for the complete specification of the system. We use the method of reduction of order to reduce the nonlinear fourth-order system to a third-order system comprising a linear second-order equation and a conservation law. We obtain the representation of the complete symmetry group from this system. Four of the required symmetries are nonlocal and the algebra is the direct sum of a one-dimensional Abelian algebra with the semidirect sum of a two-dimensional solvable algebra with a two-dimensional Abelian algebra. The problem illustrates the difficulties which can arise in very elementary systems. Our treatment demonstrates the existence of possible routes to overcome these problems in a systematic fashion.
Andriopoulos Konstantinos
Karasu Atalay
Leach P. G. L.
Nucci M. C.
No associations
LandOfFree
Ermakov's Superintegrable Toy and Nonlocal Symmetries does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Ermakov's Superintegrable Toy and Nonlocal Symmetries, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ermakov's Superintegrable Toy and Nonlocal Symmetries will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-435720