6 papers
Integrable Equations on Time Scales
Metin Gurses, Gusein Sh. Guseinov, Burcu Silindir
Integrable systems are usually given in terms of functions of continuous variables (on ), functions of discrete variables (on ) and recently in terms of f…
All Poisson Structures in
Metin Gurses, Konstantyn Zheltukhin
Hamiltonian formulation of N=3 systems is considered in general. The most general solution of the Jacobi equation in is proposed. Compatible Poisson structures and…
Sigma Models, Minimal Surfaces and Some Ricci Flat Pseudo Riemannian Geometries
Metin Gurses
We consider the sigma models where the base metric is proportional to the metric of the configuration space. We show that the corresponding sigma model equation admits a Lax pair.…
Some Ricci Flat (pseudo-) Riemannian Geometries
Metin Gurses
We define a class of two dimensional surfaces conformally related to minimal surfaces in flat three dimensional geometries. By the utility of the metrics of such surfaces we give a…
Extremely Charged Static Dust Distributions in General Relativity
Metin Gurses
Conformo static charged dust distributions are investigated in the framework of General Relativity. Einstein's equations reduce to a nonlinear version of Poisson's equations and Ma…
Sigma Models and Minimal Surfaces
Metin Gurses
The correspondance is established between the sigma models, the minimal surfaces and the Monge-Ampere equation. The Lax -Pairs of the minimality condition of the minimal surfaces a…