Now showing items 1-20 of 28

    • (2 + 1)-dimensional AKNS(−N) systems II 

      Gürses, Metin; Pekcan, Aslı (Elsevier BV, 2021-06)
      In our previous work (Gürses and Pekcan, 2019, [40]) we started to investigate negative AKNS(−N) hierarchy in (2 + 1)-dimensions. We were able to obtain only the first three, N = 0, 1, 2, members of this hierarchy. The ...
    • (2+1)-dimensional local and nonlocal reductions of the negative AKNS system: soliton solutions 

      Gürses, Metin; Pekcan, A. (Elsevier, 2018)
      Wefirstconstructa(2+1)dimensionalnegativeAKNShierarchyandthenwegiveallpossiblelocaland(discrete)nonlocalreductionsoftheseequations.WefindHirotabilinearformsofthenegativeAKNShierarchyandgiveone-andtwo-solitonsolutions.Byu ...
    • Classical double copy: Kerr-Schild-Kundt metrics from Yang-Mills theory 

      Gürses, Metin; Tekin, B. (American Physical Society, 2018)
      The classical double copy idea relates some solutions of Einstein's theory with those of gauge and scalar field theories. We study the Kerr-Schild-Kundt (KSK) class of metrics in d dimensions in the context of possible new ...
    • Comment on “Einstein-Gauss-Bonnet Gravity in four-dimensional spacetime” 

      Gürses, Metin; Şişman, T. Ç.; Tekin, B. (American Physical Society, 2020)
      We summarize our proof that the "Einstein-Gauss-Bonnet Gravity in Four-Dimensional Spacetime" introduced in Phys. Rev. Lett. 124, 081301 (2020) does not have consistent field equations, as such the theory does not exist. ...
    • Discrete symmetries and nonlocal reductions 

      Gürses, Metin; Pekcan, A.; Zheltukhin, K. (Elsevier, 2020)
      We show that nonlocal reductions of systems of integrable nonlinear partial differential equations are the special discrete symmetry transformations.
    • Extremely charged static dust distributions in general relativity 

      Gürses, Metin (World Scientific, 1998)
      Conformo static charged dust distributions are investigated in the framework of general relativity. Einstein’s equations reduce to a non-linear version of Poisson’s equation and Maxwell’s equations imply the equality of ...
    • FLRW-cosmology in generic gravity theories 

      Gürses, Metin; Heydarzade, Yaghoub (Springer Science and Business Media Deutschland GmbH, 2020-11)
      We prove that for the Friedmann–Lemaitre–Robertson–Walker metric, the field equations of any generic gravity theory in arbitrary dimensions are of the perfect fluid type. The cases of general Lovelock and F(R,G)F(R,G) ...
    • Integrable nonlocal reductions 

      Gürses, Metin; Pekcan, A. (Springer New York LLC, 2018)
      We present some nonlocal integrable systems by using the Ablowitz-Musslimani nonlocal reductions. We first present all possible nonlocal reductions of nonlinear Schrödinger (NLS) and modified Korteweg-de Vries (mKdV) ...
    • Is there a novel Einstein–Gauss–Bonnet theory in four dimensions? 

      Gürses, Metin; Şişman, T. Ç.; Tekin, B. (Springer, 2020-07)
      No! We show that the field equations of Einstein–Gauss–Bonnet theory defined in generic D>4D>4 dimensions split into two parts one of which always remains higher dimensional, and hence the theory does not have a non-trivial ...
    • Kerr–Schild–Kundt metrics in generic gravity theories with modified Horndeski couplings 

      Gürses, Metin; Heydarzade, Yaghoub; Şentürk, Çetin (Springer, 2021-12-31)
      The Kerr–Schild–Kundt (KSK) metrics are known to be one of the universal metrics in general relativity, which means that they solve the vacuum field equations of any gravity theory constructed from the curvature tensor and ...
    • A Modified Gravity Theory: Null Aether* 

      Gürses, Metin; Şentürk, Çetin (Chinese Physical Society and IOP Publishing, 2019-03)
      General quantum gravity arguments predict that Lorentz symmetry might not hold exactly in nature. This has motivated much interest in Lorentz breaking gravity theories recently. Among such models are vector-tensor theories ...
    • Motion of curves on two-dimensional surfaces and soliton equations 

      Gürses, Metin (Elsevier BV * North - Holland, 1998)
      A connection is established between the soliton equations and curves moving in a three-dimensional space V3. The signs of the self-interacting terms of the soliton equations are related to the signature of V3. It is shown ...
    • NAT black holes 

      Gürses, Metin; Heydarzade, Yaghoub; Şentürk, Ç. (Springer, 2019)
      We study some physical properties of black holes in Null Aether Theory (NAT) – a vector-tensor theory of gravity. We first review the black hole solutions in NAT and then derive the first law of black hole thermodynamics. ...
    • New classes of spherically symmetric, inhomogeneous cosmological models 

      Gürses, Metin; Heydarzade, Yaghoub (American Physical Society, 2019)
      We present two classes of inhomogeneous, spherically symmetric solutions of the Einstein-Maxwell-perfect fluid field equations with cosmological constant generalizing the Vaidya-Shah solution. Some special limits of our ...
    • New symmetries of the vacuum Einstein equations 

      Gürses, Metin (American Physical Society, 1993)
      Some new symmetry algebras are found for the vacuum Einstein equations. Among them there exists an infinite-dimensional algebra representing the symmetries analogous to the generalized symmetries of the integrable nonlinear ...
    • Non-Einsteinian black holes in generic 3D gravity theories 

      Gürses, Metin; Şişman, T. Ç.; Tekin, B. (American Physical Society, 2019)
      The Bañados-Teitelboim-Zanelli (BTZ) black hole metric solves the three-dimensional Einstein’s theory with a negative cosmological constant as well as all the generic higher derivative gravity theories based on the metric; ...
    • Nonlocal Fordy-Kulish equations on symmetric spaces 

      Gürses, Metin (Elsevier, 2017)
      We present nonlocal integrable reductions of the Fordy–Kulish system of nonlinear Schrodinger equations and the Fordy system of derivative nonlinear Schrodinger equations on Hermitian symmetric spaces. Examples are given ...
    • Nonlocal hydrodynamic type of equations 

      Gürses, Metin; Pekcan, A.; Zheltukhin, K. (Elsevier, 2020-03-01)
      We show that the integrable equations of hydrodynamic type admit nonlocal reductions. We first construct such reductions for a general Lax equation and then give several examples. The reduced nonlocal equations are of ...
    • Nonlocal KdV equations 

      Gürses, Metin; Pekcan, A. (Elsevier, 2020)
      Writing the Hirota-Satsuma (HS) system of equations in a symmetrical form we find its local and new nonlocal reductions. It turns out that all reductions of the HS system are Korteweg-de Vries (KdV), complex KdV, and new ...
    • Nonlocal modified KdV equations and their soliton solutions by Hirota Method 

      Gürses, Metin; Pekcan, A. (Elsevier, 2019)
      We study the nonlocal modified Korteweg–de Vries (mKdV) equations obtained from AKNS scheme by Ablowitz–Musslimani type nonlocal reductions. We first find soliton solutions of the coupled mKdV system by using the Hirota ...