arXiv subjects

A. H. Kara

Publications and source records attributed to A. H. Kara.

4 recordsLinked to original sources

arXiv2019

A note on some perfect fluid Kantowski-Sachs and Bianchi type III space-times and their conformal vector fields in f(R) theory of gravity

The purpose of this paper is to find conformal vector fields of some perfect fluid Kantowski-Sachs and Bianchi type III space-times in the f(R) theory of gravity using direct integration technique. In this study there exists only eight cases. Studying each case in detail, we found that in two cases proper conformal vector fields exist while in the rest of six cases conformal vector fields become Killing vector fields. The dimension of conformal vector fields is either 4 or 6.

gr-qc↗

arXiv2017

Symmetry Analysis and Conservation Laws of some third-order Difference Equations

We derive a method for finding Lie Symmetries for third-order difference equations. We use these symmetries to reduce the order of the difference equations and hence obtain the solutions of some third-order difference equations. We also introduce a technique for obtaining their first integrals.

nlin.SI↗

arXiv2016

Some geometric structures of wave equations on manifolds of `neutral signatures'

In this paper, we study the symmetries and perform other geometric analyses of the wave equation on some spacetimes {with non diagonal metric $g_{ij}$ which are of neutral signatures}. Wave equations on the standard Lorentzian manifolds have been done but not on the manifolds from metrics of neutral signatures.

math-ph↗

arXiv2009

Generalization of the double reduction theory

In a recent work [1, 2] Sjoberg remarked that generalization of the double reduction theory to partial differential equations of higher dimensions is still an open problem. In this note we have attempted to provide this generalization to find invariant solution for a non linear system of qth order partial differential equations with n independent and m dependent variables provided that the non linear system of partial differential equations admits a nontrivial conserved form which has at least one associated symmetry in every reduction. In order to give an application of the procedure we apply it to the nonlinear (2 + 1) wave equation for arbitrary function f (u) and g(u).

math.AP↗