The Lie algebra sl(2,R) and so-called Kepler-Ermakov systems

Date

2004-05-01

Author

Leach, PGL
Karasu, Emine Ayşe

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

251
views

0
downloads

A recent paper by Karasu (Kalkanli) and Yildirim (Journal of Nonlinear Mathematical Physics 9 (2002) 475-482) presented a study of the Kepler-Ermakov system in the context of determining the form of an arbitrary function in the system which was compatible with the presence of the sl(2, R) algebra characteristic of Ermakov systems and the existence of a Lagrangian for a subset of the systems. We supplement that analysis by correcting some results.

Subject Keywords

Mathematical Physics, Statistical and Nonlinear Physics

URI

https://hdl.handle.net/11511/34308

Journal

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS

DOI

https://doi.org/10.2991/jnmp.2004.11.2.11

Collections

Department of Physics, Article

Suggestions

OpenMETU
Core

The path integral quantization and the construction of the S-matrix operator in the Abelian and non-Abelian Chern-Simons theories Fainberg, VY; Pak, Namık Kemal; Shikakhwa, MS (IOP Publishing, 1997-06-07) The covariant path integral quantization of the theory of the scalar and spinor fields interacting through the Abelian and non-Abelian Chern-Simons gauge fields in 2 + 1 dimensions is carried out using the De Witt-Fadeev-Popov method. The mathematical ill-definiteness of the path integral of theories with pure Chern-Simons' fields is remedied by the introduction of the Maxwell or Maxwell-type (in the non-Abelian case) terms, which make the resulting theories super-renormalizable and guarantees their gauge-i...
Quantum duality, unbounded operators, and inductive limits Dosi, Anar (AIP Publishing, 2010-06-01) In this paper, we investigate the inductive limits of quantum normed (or operator) spaces. This construction allows us to treat the space of all noncommutative continuous functions over a quantum domain as a quantum (or local operator) space of all matrix continuous linear operators equipped with G-quantum topology. In particular, we classify all quantizations of the polynormed topologies compatible with the given duality proposing a noncommutative Arens-Mackey theorem. Further, the inductive limits of oper...
A new integrable generalization of the Korteweg-de Vries equation Karasu-Kalkanli, Ayse; Karasu, Atalay; Sakovich, Anton; Sakovich, Sergei; TURHAN, REFİK (AIP Publishing, 2008-07-01) A new integrable sixth-order nonlinear wave equation is discovered by means of the Painleve analysis, which is equivalent to the Korteweg-de Vries equation with a source. A Lax representation and an auto-Backlund transformation are found for the new equation, and its traveling wave solutions and generalized symmetries are studied. (C) 2008 American Institute of Physics.
Time-dependent recursion operators and symmetries Gurses, M; Karasu, Atalay; Turhan, R (Informa UK Limited, 2002-05-01) The recursion operators and symmetries of nonautonomous, (1 + 1) dimensional integrable evolution equations are considered. It has been previously observed hat he symmetries of he integrable evolution equations obtained through heir recursion operators do not satisfy the symmetry equations. There have been several attempts to resolve his problem. It is shown that in the case of time-dependent evolution equations or time-dependent recursion operators associativity is lost. Due to this fact such recursion ope...
Dynamical systems and Poisson structures Guerses, Metin; Guseinov, Gusein Sh; Zheltukhın, Kostyantyn (AIP Publishing, 2009-11-01) We first consider the Hamiltonian formulation of n=3 systems, in general, and show that all dynamical systems in R-3 are locally bi-Hamiltonian. An algorithm is introduced to obtain Poisson structures of a given dynamical system. The construction of the Poisson structures is based on solving an associated first order linear partial differential equations. We find the Poisson structures of a dynamical system recently given by Bender et al. [J. Phys. A: Math. Theor. 40, F793 (2007)]. Secondly, we show that al...

Citation Formats

P. Leach and E. A. Karasu, “The Lie algebra sl(2,R) and so-called Kepler-Ermakov systems,” JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, pp. 269–275, 2004, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/34308.