Atalay Karasu

Department of Physics
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Minimal extension of Einstein's theory: The quartic gravity
Karasu, Atalay; Kenar, Esin; Tekin, Bayram (2016-04-20)
We study structure of solutions of the recently constructed minimal extensions of Einstein's gravity in four dimensions at the quartic curvature level. The extended higher derivative theory, just like Einstein's gravity, h...
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 s...
Nonlocal symmetries and integrable ordinary differential equations: xuml+3xx center dot+x(3)=0 and its generalizations
Karasu, Atalay; Leach, P. G. L. (AIP Publishing, 2009-07-01)
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 le...
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 transform...
Gardner's deformations of the Boussinesq equations
Karasu, Atalay; Kiselev, Arthemy V. (IOP Publishing, 2006-09-15)
Using the algebraic method of Gardner's deformations for completely integrable systems, we construct recurrence relations for densities of the Hamiltonians for the Boussinesq and the Kaup-Boussinesq equations. By extending...
Closed timelike curves and geodesics of Godel-type metrics
Gleiser, RJ; Gurses, M; Karasu, Atalay; Sarıoğlu, Bahtiyar Özgür (IOP Publishing, 2006-04-07)
it is shown explicitly that when the characteristic vector field that defines a Godel-type metric is also a Killing vector, there always exist closed timelike or null curves in spacetimes described by such a metric. For th...
Gödel-type metrics in various dimensions
Gürses, Metin; Karasu, Atalay; Sarıoğlu, Bahtiyar Özgür (IOP Publishing, 2005-4-6)
Godel-type metrics are introduced and used in producing charged dust solutions in various dimensions. The key ingredient is a (D-1)-dimensional Riemannian geometry which is then employed in constructing solutions to the Ei...
Ermakov's Superintegrable Toy and Nonlocal Symmetries
Leach, P. G. L.; Karasu, Atalay; Nucci, M. C.; Andriopoulos, K. (SIGMA (Symmetry, Integrability and Geometry: Methods and Application), 2005-01-01)
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 insufficie...
A strange recursion operator for a new integrable system of coupled Korteweg-de Vries equations
Karasu, A; Karasu, Atalay; Sakovich, SY (Springer Science and Business Media LLC, 2004-08-01)
A recursion operator is constructed for a new integrable system of coupled Korteweg de Vries equations by the method of gauge-invariant description of zero-curvature representations. This second-order recursion operator is...
Integrability of a nonautonomous coupled KdV system
Karasu, Atalay; Kilic, T (2004-06-01)
The Painleve property of coupled, nonautonomous Korteweg-de Vries (KdV) type of systems is studied. The conditions under which the systems pass the Painleve test for integrability axe obtained. For some of the integrable c...
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