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
Time-dependent recursion operators and symmetries
Download
index.pdf
Date
2002-05-01
Author
Gurses, M
Karasu, Atalay
Turhan, R
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
286
views
104
downloads
Cite This
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 operators need modi cation. A general formula is given for he missing term of the recursion operators. Apart from he recursion operators a method is introduced to calculate the correct symmetries. For illustrations several examples of scalar and coupled system of equations are considered.
Subject Keywords
Mathematical Physics
,
Statistical and Nonlinear Physics
URI
https://hdl.handle.net/11511/34580
Journal
JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS
DOI
https://doi.org/10.2991/jnmp.2002.9.2.5
Collections
Department of Physics, Article
Suggestions
OpenMETU
Core
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...
ON NON-COMMUTATIVE INTEGRABLE BURGERS EQUATIONS
GÜRSES, METİN; Karasu, Atalay; TURHAN, REFİK (Informa UK Limited, 2010-03-01)
We construct the recursion operators for the non-commutative Burgers equations using their Lax operators. We investigate the existence of any integrable mixed version of left- and right-handed Burgers equations on higher symmetry grounds.
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...
Hydrodynamic type integrable equations on a segment and a half-line
Guerses, Metin; Habibullin, Ismagil; Zheltukhın, Kostyantyn (AIP Publishing, 2008-10-01)
The concept of integrable boundary conditions is applied to hydrodynamic type systems. Examples of such boundary conditions for dispersionless Toda systems are obtained. The close relation of integrable boundary conditions with integrable reductions in multifield systems is observed. The problem of consistency of boundary conditions with the Hamiltonian formulation is discussed. Examples of Hamiltonian integrable hydrodynamic type systems on a segment and a semiline are presented. (C) 2008 American Institut...
Symmetry reductions of a Hamilton-Jacobi-Bellman equation arising in financial mathematics
Naicker, V; Andriopoulos, K; Leach, PGL (Informa UK Limited, 2005-05-01)
We determine the solutions of a nonlinear Hamilton-Jacobi-Bellman equation which arises in the modelling of mean-variance hedging subject to a terminal condition. Firstly we establish those forms of the equation which admit the maximal number of Lie point symmetries and then examine each in turn. We show that the Lie method is only suitable for an equation of maximal symmetry. We indicate the applicability of the method to cases in which the parametric function depends also upon the time.
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
M. Gurses, A. Karasu, and R. Turhan, “Time-dependent recursion operators and symmetries,”
JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS
, pp. 210–228, 2002, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/34580.