Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Nonlocal symmetries and integrable ordinary differential equations: xuml+3xx center dot+x(3)=0 and its generalizations
Date
2009-07-01
Author
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
203
views
0
downloads
Cite This
The equation xuml+3xx center dot+x(3)=0 is well known in many areas of mathematics and physics. It possesses the algebra sl(3,R) of Lie point symmetries, hence is equivalent to the equation for a free particle, and both left and right Painleveacute series. We investigate two higher-dimensional analogs in terms of their symmetry and singularity structures. We find a drastic reduction in symmetry and a loss of some of the singularity properties. From the nonlocal symmetries we are able to determine the complete symmetry group as being represented by a five-dimensional Abelian algebra.
Subject Keywords
Mathematical Physics
,
Statistical and Nonlinear Physics
URI
https://hdl.handle.net/11511/35445
Journal
JOURNAL OF MATHEMATICAL PHYSICS
DOI
https://doi.org/10.1063/1.3158856
Collections
Department of Physics, Article
Suggestions
OpenMETU
Core
Hamiltonian equations in R-3
Ay, Ahmet; GÜRSES, METİN; Zheltukhın, Kostyantyn (AIP Publishing, 2003-12-01)
The Hamiltonian formulation of N=3 systems is considered in general. The most general solution of the Jacobi equation in R-3 is proposed. The form of the solution is shown to be valid also in the neighborhood of some irregular points. Compatible Poisson structures and corresponding bi-Hamiltonian systems are also discussed. Hamiltonian structures, the classification of irregular points and the corresponding reduced first order differential equations of several examples are given. (C) 2003 American Institute...
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...
The Lie algebra sl(2,R) and so-called Kepler-Ermakov systems
Leach, PGL; Karasu, Emine Ayşe (Informa UK Limited, 2004-05-01)
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.
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.
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
E. A. Karasu, “Nonlocal symmetries and integrable ordinary differential equations: xuml+3xx center dot+x(3)=0 and its generalizations,”
JOURNAL OF MATHEMATICAL PHYSICS
, pp. 0–0, 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/35445.