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Sep 22, 2013
09/13

by
R. Myrzakulov

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Gauge equivalence between the two-dimensional continuous classical Heisenberg ferromagnets(CCHF) of spin 1/2 - the M-I equation with single site anisotropy and the Zakharov equation(ZE) is established for the easy axis case. The anisotropic CCHF is shown to be gauge equivalent to the isotropic CCHF.

Source: http://arxiv.org/abs/cond-mat/9805188v1

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79

Sep 23, 2013
09/13

by
R. Myrzakulov

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The (2+1)-dimensional integrable M-XX equation is considered.

Source: http://arxiv.org/abs/solv-int/9904011v1

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42

Sep 22, 2013
09/13

by
R. Myrzakulov

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The gauge equivalence between the (2+1)-dimensional Zakharov equations and (2+1)-dimensional integrable continuous Heisenberg ferromagnetic model is established. Also their integrable reductions are shown explicitly.

Source: http://arxiv.org/abs/cond-mat/9805187v1

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53

Sep 24, 2013
09/13

by
R. Myrzakulov

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The vortex filament equations (VFE) in 1+1 and 2+1 dimensions are considered. Some of these equations are integrable. Also the VFE with potentials and with self-consistent potentials are presented. Finally several examples of integrable dispersionless VFE (dVFE) are considered.

Source: http://arxiv.org/abs/physics/0412153v1

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Sep 18, 2013
09/13

by
R. Myrzakulov

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The (2+1)-dimensional integrable Zakharov equations and their reductions are considered

Source: http://arxiv.org/abs/solv-int/9903008v1

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58

Sep 19, 2013
09/13

by
R. Myrzakulov

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The gauge equivalent counterparts of the some (1+1)-, or (2+0)-dimensional sigma models with potentials are found. The gauge equivalence between the some soliton equations of spin-phonon systems and the Yajima-Oikawa and Ma equations are also established.

Source: http://arxiv.org/abs/hep-th/9812214v1

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36

Sep 22, 2013
09/13

by
R. Myrzakulov

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Using the differential geometry of curves and surfaces the Lakshmanan equivalent counterpart of the M-XXII equation is found ... .

Source: http://arxiv.org/abs/math-ph/9807033v1

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42

Sep 23, 2013
09/13

by
R. Myrzakulov

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A connection between differential geometry and soliton equations is discussed

Source: http://arxiv.org/abs/math/9908155v1

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58

Sep 20, 2013
09/13

by
R. Myrzakulov

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The briefly review on the common spin description of the nonlinear evolution equations.

Source: http://arxiv.org/abs/solv-int/9802017v1

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67

Sep 23, 2013
09/13

by
R. Myrzakulov; M. Shahalam

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In this paper, we use statefinder hierarchy method to distinguish between bimetric theory of massive gravity and DGP model applied to late time expansion of universe. We also carry out comparison of bimetric model and galileon system . We show that statefinder diagnostic can differentiate between the currently discussed cosmological models.

Source: http://arxiv.org/abs/1303.0194v2

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121

Sep 18, 2013
09/13

by
Kuralay Myrzakul; R. Myrzakulov

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The L-equivalent counterpart of the M-LXIX equation is found. This L-equivalent equation is the Gauss-Codazzi equation which is integrable by the dressing method. This means that the M-LXIX equation is also integrable in this sense.

Source: http://arxiv.org/abs/math/0110062v1

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7.0

Jun 30, 2018
06/18

by
D. Momeni; R. Myrzakulov

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Based on a stringy inspired Gauss-Bonnet (GB) modification of classical gravity, we constructed a model for neutron stars. We derived the modified forms of Tolman-Oppenheimer-Volkoff (TOV) equations for a generic function of $f(G)$ gravity. The hydrostatic equations remained unchanged but the dynamical equations for metric functions are modified due to the effects of GB term.

Topics: High Energy Physics - Theory, High Energy Astrophysical Phenomena, Astrophysics, General Relativity...

Source: http://arxiv.org/abs/1408.3626

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70

Sep 19, 2013
09/13

by
Kur. Myrzakul; R. Myrzakulov

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Some aspects of the multidimensional soliton geometry are considered. The relation between soliton equations in 2+1 dimensions and the Self-Dual Yang-Mills and Bogomolny equations are discussed.

Source: http://arxiv.org/abs/math-ph/9911003v1

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5.0

Jun 30, 2018
06/18

by
R. Myrzakulov; M. Shahalam

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We study Galileon scalar field model by considering the lowest order Galileon term in the lagrangian, $(\partial_{\mu} \phi)^2 \Box\phi$ by invoking a field potential. We use Statefinder hierarchy to distinguish the light mass galileon models with different potentials amongst themselves and from the $\Lambda$CDM behaviour. The $Om$ diagnostic is applied to cosmological dynamics and observational constraints on the model parameters are studied using SN+Hubble+BAO data.

Topics: Astrophysics, General Relativity and Quantum Cosmology, Cosmology and Nongalactic Astrophysics

Source: http://arxiv.org/abs/1407.7798

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96

Sep 17, 2013
09/13

by
Kur. Myrzakul; R. Myrzakulov

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Some aspects of multidimensional soliton geometry are considered.

Source: http://arxiv.org/abs/gr-qc/0007043v1

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Jun 28, 2018
06/18

by
M. Khurshudyan; R. Myrzakulov

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Varying Chaplygin gas is one of the dark fluids actively studied in modern cosmology. It does belong to the group of the fluids which has an explicitly given EoS. From the other hand phase space does contain all possible states of the system. Therefore, phase space analysis of the cosmological models does allow to understand qualitative behavior and estimate required characteristics of the models. Phase space analysis is a convenient approach to study a cosmological model, because we do not...

Topic: General Relativity and Quantum Cosmology

Source: http://arxiv.org/abs/1509.07357

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6.0

Jun 30, 2018
06/18

by
D. Momeni; R. Myrzakulov

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In this letter we study aspects of the holographic superconductors analytically in the presence of a constant external magnetic field. We show that the critical temperature and critical magnetic field can be calculated at nonzero temperature. We detect the Meissner effect in such superconductors. A universal relation between black hole mass $ M$ and critical magnetic field $H_c$ is proposed as $\frac{H_c}{M^{2/3}}\leq 0.687365$. We discuss some aspects of phase transition in terms of black hole...

Topic: High Energy Physics - Theory

Source: http://arxiv.org/abs/1401.3658

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59

Sep 17, 2013
09/13

by
Kur. Myrzakul; R. Myrzakulov

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The connection between multidimensional soliton equations and three-dimensional Riemann space is discussed.

Source: http://arxiv.org/abs/gr-qc/0007012v1

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Sep 17, 2013
09/13

by
R. Myrzakulov; Kur. Myrzakul

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Integrability of the (2+1)-dimensional Gauss-Codazzi-Mainardi equation is considered. It is shown that this equation is the particular cases of the Yang-Mills-Higgs-Bogomolny and self-dual Yang-Mills equations.

Source: http://arxiv.org/abs/math/0108128v1

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17

Jun 28, 2018
06/18

by
M. Khurshudyan; R. Myrzakulov

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The goal of this paper is to discuss phase space analysis of some interacting Chaplygin gas models in General Relativity. Chaplygin gas is one of the fluids actively considered in modern cosmology due to the fact that it is a joint model of dark energy and dark matter. In this paper we have considered various forms of interaction term Q including linear and non linear sign changeable interactions. For each case late time attractors for the field equations are found.

Topic: General Relativity and Quantum Cosmology

Source: http://arxiv.org/abs/1509.02263

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85

Jul 20, 2013
07/13

by
Kur. R. Myrzakul; R. Myrzakulov

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Some aspects of the relation between differential geometry of curves and surfaces and multidimensional soliton equations is discussed. The connection between multidimensional soliton equations and Self-dual Yang-Mills equation is studied.

Source: http://arxiv.org/abs/math/9910125v1

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52

Sep 18, 2013
09/13

by
Kur. R. Myrzakul; R. Myrzakulov

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Some aspects of the multidimensional soliton geometry are considered. It is shown that some simples (2+1)-dimensional equations are exact reductions of the Self-Dual Yang-Mills equation or its higher hierarchy.

Source: http://arxiv.org/abs/math-ph/0002019v1

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57

Sep 18, 2013
09/13

by
S. C. Anco; R. Myrzakulov

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A moving frame formulation of non-stretching geometric curve flows in Euclidean space is used to derive a 1+1 dimensional hierarchy of integrable SO(3)-invariant vector models containing the Heisenberg ferromagnetic spin model as well as a model given by a spin-vector version of the mKdV equation. These models describe a geometric realization of the NLS hierarchy of soliton equations whose bi-Hamiltonian structure is shown to be encoded in the Frenet equations of the moving frame. This...

Source: http://arxiv.org/abs/0806.1360v4

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66

Sep 23, 2013
09/13

by
R. Myrzakulov; A. K. Danlybaeva

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The connection between differential geometry of curves and the (2+1)-dimensional integrable spin system - the M-III equation is established. Using the presented geometrical formalism the L-equivalent counterpart of the M-III equation is found.

Source: http://arxiv.org/abs/math/9909155v1

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100

Sep 17, 2013
09/13

by
V. Dzhunushaliev; N. Serikbayev; R. Myrzakulov

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The topology change in quantum gravity is modeled by a Ricci flow. In this approach we offer to consider the Ricci flow as a statistical system. The metric in the Ricci flow enumerated by a parameter $\lambda$ is a microscopical statistical state. The probability of every microscopical state is determined by the parameter $\lambda$. Numerically the Ricci flow starting from a static wormhole filled with a phantom Sine-Gordon scalar field is investigated.

Source: http://arxiv.org/abs/0912.5326v2

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46

Sep 23, 2013
09/13

by
V. Dzhunushaliev; I. Kulnazarov; R. Myrzakulov

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A regular wormhole solution in gravity coupled with a phantom scalar and electromagnetic fields is found. The solution exists for a special choice of the parameter $f$ of the potential term. The mass $m$ of a wormhole filled with a phantom and electrostatic fields is calculated. It is shown that close to some point $f_0$ a small value of the mass $m$ is the remainder of two big masses of the phantom and electrostatic fields. The connection with the renormalization procedure in quantum filed...

Source: http://arxiv.org/abs/1006.0599v3

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47

Sep 22, 2013
09/13

by
V. Dzhunushaliev; V. Folomeev; R. Myrzakulov

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Eigenvalue problem for two coupled Ginzburg-Landau equations is numerically investigated. The fixed points of corresponding equations system are found. The classification of these points is made. The phase portraits of corresponding ordinary differential equations and the dependence of some parameters of the equations system and the total energy on the initial values are given.

Source: http://arxiv.org/abs/1103.5315v1

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114

Jul 20, 2013
07/13

by
V. Dzhunushaliev; K. Myrzakulov; R. Myrzakulov

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The boson star filled with two interacting scalar fields is investigated. The scalar fields can be considered as a gauge condensate formed by SU(3) gauge field quantized in a non-perturbative manner. The corresponding solution is regular everywhere, has a finite energy and can be considered as a quantum SU(3) version of the Bartnik - McKinnon particle-like solution.

Source: http://arxiv.org/abs/gr-qc/0604110v6

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55

Sep 21, 2013
09/13

by
D. Momeni; N. Majd; R. Myrzakulov

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We study the (3+1) dimensional p-wave holographic superconductors with Weyl corrections both numerically and analytically. We describe numerically the behavior of critical temperature $T_{c}$ with respect to charge density $\rho$ in a limited range of Weyl coupling parameter $\gamma$ and we find in general the condensation becomes harder with the increase of parameter $\gamma$. In strong coupling limit of Yang-Mills theory, we show that the minimum value of $T_{c}$ obtained from analytical...

Source: http://arxiv.org/abs/1204.1246v2

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46

Sep 17, 2013
09/13

by
V. Dzhunushaliev; K. Myrzakulov; R. Myrzakulov

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The model of dark matter is presented where the dark matter is a \emph{classical} gauge field. A spherical symmetric solution of Yang-Mills equation is obtained. The asymptotic behavior of the gauge fields and matter density is investigated. It is shown that the distribution of the matter density allows us interpret it as the dark matter. The fitting of a typical rotational curve with the rotational curve created by the spherical solution of SU(3) Yang-Mills equation is made.

Source: http://arxiv.org/abs/0912.4311v3

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7.0

Jun 29, 2018
06/18

by
L. Sebastiani; S. Vagnozzi; R. Myrzakulov

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Mimetic gravity is a Weyl-symmetric extension of General Relativity, related to the latter by a singular disformal transformation, wherein the appearance of a dust-like perfect fluid can mimic cold dark matter at a cosmological level. Within this framework, it is possible to provide an unified geometrical explanation for dark matter, the late-time acceleration, and inflation, making it a very attractive theory. In this review, we summarize the main aspects of mimetic gravity, as well as...

Topic: General Relativity and Quantum Cosmology

Source: http://arxiv.org/abs/1612.08661

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77

Sep 22, 2013
09/13

by
Mubasher Jamil; D. Momeni; R. Myrzakulov

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In this paper, we investigate the Noether symmetries of $F(T)$ cosmology involving matter and dark energy. In this model, the dark energy is represented by a canonical scalar field with a potential. Two special cases for dark energy are considered including phantom energy and quintessence. We obtain $F(T)\sim T^{3/4},$ and the scalar potential $V(\phi)\sim\phi^2$ for both models of dark energy and discuss quantum picture of this model. Some astrophysical implications are also discussed.

Source: http://arxiv.org/abs/1210.0001v1

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8.0

Jun 26, 2018
06/18

by
D. Momeni; R. Myrzakulov; E. Güdekli

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Extended $f(R)$ theories of gravity have been investigated from the symmetry point of view. We briefly has been investigated Noether symmetry of two types of extended $f(R)$ theories: $f(R,T)$ theory, in which curvature is coupled non minimally to the trace of energy momentum tensor $T_{\mu\nu}$ and mimetic $f (R) $ gravity, a theory with a scalar field degree of freedom, but ghost-free and with internal conformal symmetry. In both cases we write point -like Lagrangian for flat...

Topic: General Relativity and Quantum Cosmology

Source: http://arxiv.org/abs/1502.00977

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47

Sep 17, 2013
09/13

by
L. Martina; Kur. Myrzakul; R. Myrzakulov

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The study of the relation between the Weierstrass inducing formulae for constant mean curvature surfaces and the completely integrable euclidean nonlinear sigma-model suggests a connection among integrable sigma -models in a background and other type of surfaces. We show how a generalization of the Weierstrass representation can be achieved and we establish a connection with the Weingarten surfaces. We suggest also a possible generalization for two-dimensional surfaces immersed in a flat space...

Source: http://arxiv.org/abs/math/0207261v1

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5.0

Jun 30, 2018
06/18

by
H. Gholizade; A. Altaibayeva; R. Myrzakulov

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We study thermodynamic of strange quark matter (SQM) using the analytic expressions of free and internal energies. We investigate two regimes of the high density and low density separately. As a vital program, in the case of a massless gluon and massless quarks at finite temperature, we also present a geometry of thermodynamics for the gluon and Bosons using a Legendre invariance metric, it is so called as geometrothermodynamic (GTD) to better understanding of the phase transition. The GTD...

Topic: General Relativity and Quantum Cosmology

Source: http://arxiv.org/abs/1412.6819

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5.0

Jun 28, 2018
06/18

by
Safia Ahmad; Nurgissa Myrzakulov; R. Myrzakulov

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In this paper, we consider rolling tachyon, with steep run-away type of potentials non-minimally coupled to massive neutrino matter. The coupling dynamically builds up at late times as neutrino matter turns non-relativistic. In case of scaling and string inspired potentials, we have shown that non-minimal coupling leads to minimum in the field potential. Given a suitable choice of model parameters, it is shown to give rise to late-time acceleration with the desired equation of state.

Topics: High Energy Physics - Theory, Cosmology and Nongalactic Astrophysics, Astrophysics, General...

Source: http://arxiv.org/abs/1510.04795

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44

Sep 23, 2013
09/13

by
V. Dzhunushaliev; V. Folomeev; R. Myrzakulov

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A self-similar motion of the generalized Chaplygin gas in its own gravitational field is considered. The problem is being studied numerically and analytically (in the limiting cases). It is shown that the model under consideration admits only expanding solutions. As the astrophysical application of the model, a description of rotating curves of spiral galaxies is suggested by using the analytical solutions obtained in the paper.

Source: http://arxiv.org/abs/1006.1463v2

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59

Sep 22, 2013
09/13

by
M. Sharif; S. Rani; R. Myrzakulov

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This paper is devoted to study the energy conditions in F(R,T) gravity for FRW universe with perfect fluid, where $R$ is the Ricci scalar and $T$ is the torsion scalar. We construct the general energy conditions in this theory and reduce them in F(R) as well as F(T) theory of gravity. Further, we assume some viable models and investigate bounds on their constant parameters to satisfy the energy condition inequalities. We also plot some of the cases using present-day values of the cosmological...

Source: http://arxiv.org/abs/1210.2714v1

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9.0

Jun 27, 2018
06/18

by
R. Myrzakulov; L. Sebastiani; S. Vagnozzi

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We investigate inflation within $f(R,\phi)$-theories, where a dynamical scalar field is coupled to gravity. A class of models which can support early-time acceleration with the emerging of an effective cosmological constant at high curvature is studied. The dynamics of the field allow for exit from inflation leading to the correct amount of inflation in agreement with cosmological data. Furthermore, the spectral index and tensor-to-scalar ratio of the models are carefully analyzed. A...

Topic: General Relativity and Quantum Cosmology

Source: http://arxiv.org/abs/1504.07984

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92

Sep 18, 2013
09/13

by
Mubasher Jamil; D. Momeni; R. Myrzakulov

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In this Letter, we derived the first law of thermodynamics using the method proposed by Wald. Treating the entropy as Noether charge and comparing with the usual first law of thermodynamics, we obtained the expression of entropy explicitly which contains infinitely many non-local terms (i.e. the integral terms). We have proved, in general, that the first law of black bole thermodynamics is violated for $f(R,T)$ gravity. But there might exist some special cases in which the first law for...

Source: http://arxiv.org/abs/1209.2916v2

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6.0

Jun 30, 2018
06/18

by
G. C. Samanta; Mayank Goel; R. Myrzakulov

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In this paper an explicit cosmological model which allows cosmological singularities are discussed. The generalized power-law and asymptotic expansions of the baro-tropic fluid index $\omega$ and equivalently the deceleration parameter $q$, in terms of cosmic time $'t'$ are considered. Finally, the strength of the found singularities is discussed.

Topic: General Relativity and Quantum Cosmology

Source: http://arxiv.org/abs/1703.00239

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44

Sep 17, 2013
09/13

by
T. A. Kozhamkulov; Kuralay Myrzakul; R. Myrzakulov

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We conjecture that many (maybe all) integrable equations and spin systems in 2+1 dimensions can be obtained from the (2+1)-dimensional Gauss-Mainardi-Codazzi and Gauss-Weingarten equations, respectively. We also show that the (2+1)-dimensional Gauss-Mainardi-Codazzi equation which describes the deformation (motion) of surfaces is the exact reduction of the Yang-Mills-Higgs-Bogomolny and Self-Dual Yang-Mills equations. On the basis of this observation, we suggest that the (2+1)-dimensional...

Source: http://arxiv.org/abs/nlin/0207046v1

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44

Sep 22, 2013
09/13

by
M. R. Setare; D. Momeni; R. Myrzakulov

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In this short letter we calculate separately the generalized uncertainty principle (GUP) and self gravitational corrections to the Newton's gravitational formula. We show that for a complete description of the GUP and self-gravity effects, both temperature and the entropy must be modified.

Source: http://arxiv.org/abs/1004.2794v2

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3.0

Jun 29, 2018
06/18

by
G. C. Samanta; R. Myrzakulov; Parth Shah

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The authors considered the bulk viscous fluid in $f(R, T)$ gravity within the framework of Kaluza-Klein space time. The bulk viscous coefficient $(\xi)$ expressed as $\xi=\xi_0+\xi_1\frac{\dot{a}}{a}+\xi_2\frac{\ddot{a}}{\dot{a}}$, where $\xi_0$, $\xi_1$ and $\xi_2$ are positive constants. We take $p=(\gamma-1)\rho$, where $0\le\gamma\le2$ as an equation of state for perfect fluid. The exact solutions to the corresponding field equations are given by assuming a particular model of the form of...

Topic: General Relativity and Quantum Cosmology

Source: http://arxiv.org/abs/1612.01121

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4.0

Jun 29, 2018
06/18

by
V. G. Makhankov; R. Myrzakulov; O. K. Pashaev

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An integrable generalization of the continuous classical O$(2,1)$ pseudospin Heisenberg model to the case of the ospu$(1,1/1)$ superalgebra is constructed. The gauge equivalence of the constructed model and the related NLSE is established. We indicate a method of generating classical solutions using the global ospu$(1,1/1)$ supersymmetry. The relationship between solutions of O$(2,1)$ HM and 'superpartners' of NLSE is obtained.

Topics: Exactly Solvable and Integrable Systems, Nonlinear Sciences

Source: http://arxiv.org/abs/1612.09124

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3.0

Jun 30, 2018
06/18

by
G. Shaikhova; K. Yesmakhanova; G. Mamyrbekova; R. Myrzakulov

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In this paper, we construct a Darboux transformation (DT) of the (2+1)-dimensional Schr\"odinger-Maxwell-Bloch equation (SMBE) which is integrable by the Inverse Scattering Method. Using this DT, the one-soliton solution and periodic solution are obtained from the "seed" solutions.

Topics: Nonlinear Sciences, Exactly Solvable and Integrable Systems

Source: http://arxiv.org/abs/1402.4669

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5.0

Jun 29, 2018
06/18

by
M. Shahalam; S. K. J. Pacif; R. Myrzakulov

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In this paper we study cosmological dynamics of phantom as well as non-phantom fields with linear potential in presence of Galileon correction $(\partial_\mu\phi \partial^\mu\phi) \Box \phi$. We show that the Big Crunch singularity is delayed compared to the standard case; the delay crucially depends upon the strength of Galileon correction. As for the phantom Galileon, $\rho_{\phi}$ is shown to grow more slowly compared to the standard phantom delaying the approach to singularity. In case,...

Topics: High Energy Physics - Theory, General Relativity and Quantum Cosmology

Source: http://arxiv.org/abs/1602.03176

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6.0

Jun 30, 2018
06/18

by
S. K. J. Pacif; K. Myrzakulov; R. Myrzakulov

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We reconstruct the field potentials in case of (non)phantom fields for different models resulting from parametrization of q(t), a(t) or H(t). In addition we carry out similar procedure for tachyonic field. We also discuss specific form of parametrization for reconstruction of scalar field potential.

Topic: General Relativity and Quantum Cosmology

Source: http://arxiv.org/abs/1702.01028

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3.0

Jun 30, 2018
06/18

by
M. Zhassybayeva; G. Mamyrbekova; G. Nugmanova; R. Myrzakulov

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The Myrzakulov-Lakshmanan-II (ML-II) equation is one of a (2+1)-dimensional generalizations of the Heisenberg ferromagnetic equation. It is integrable and has a non-isospectral Lax representation. In this paper, the Darboux transformation (DT) for the ML-II equation is constructed. Using the DT, the 1-soliton and 2-soliton solutions of the ML-II equation are presented.

Topics: Nonlinear Sciences, Exactly Solvable and Integrable Systems

Source: http://arxiv.org/abs/1404.7733

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42

Sep 19, 2013
09/13

by
V. Dzhunushaliev; V. Folomeev; K. Myrzakulov; R. Myrzakulov

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The model of cosmic string formed from two gravitating and interacting scalar fields is considered. It is shown that the regular solutions exist at special choice of the model's parameters only.

Source: http://arxiv.org/abs/gr-qc/0610111v3