Karasu, Atalay
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.


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...
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 the integrability of a class of Monge-Ampere equations
BRUNELLI, J C; GÜRSES, METİN; Zheltukhın, Kostyantyn (World Scientific Pub Co Pte Lt, 2001-04-01)
We give the Lax representations for the elliptic, hyperbolic and homogeneous second order Monge-Ampere equations. The connection between these equations and the equations of hydrodynamical type give us a scalar dispersionless Lax representation. A matrix dispersive Lax representation follows from the correspondence between sigma models, a two parameter equation for minimal surfaces and Monge-Ampere equations. Local as well nonlocal conserved densities are obtained.
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.
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
M. GÜRSES, A. Karasu, and R. TURHAN, “ON NON-COMMUTATIVE INTEGRABLE BURGERS EQUATIONS,” JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, pp. 1–6, 2010, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/34783.