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Papers by Zhanar Umurzakhova

Research paper thumbnail of Initial conditions of pre-inflation with Hilltop potential in loop quantum cosmology

arXiv (Cornell University), Aug 12, 2021

In this paper, we investigate the dynamics of pre-inflation with Hilltop potential in the framewo... more In this paper, we investigate the dynamics of pre-inflation with Hilltop potential in the framework of loop quantum cosmology. The initial conditions of inflaton field at the quantum bounce is categorized into two classes, first one is dominated by kinetic energy and second one by potential energy. In both cases, the physically viable initial values of inflaton field at the bounce are obtained numerically that generate the desired slow-roll inflation and also sufficient number of e-folds. To be consistent with observations at least 60 e-folds are required. In case of kinetic energy dominated initial conditions of inflaton field at the bounce, the numerical evolution of the background prior to preheating is divided into three different regions: bouncing, transition and slow-roll inflation whereas bouncing and transition phases disappear in the potential energy dominated case but still slow-roll inflation is achieved. This is true in case of p = 4 and v = 1M P l of Hilltop potential. However for other cases, slow-roll inflation can not be obtained. Moreover, we study the phase space analysis for Hilltop potential and discuss the phase space trajectories under the chosen parameters.

Research paper thumbnail of Nonlocal Schrödinger-Maxwell-Bloch Equations

Journal of Physics: Conference Series, 2021

In this paper we research the (1+1)-dimensional system of Schrodinger-Maxwell-Bloch equations (NL... more In this paper we research the (1+1)-dimensional system of Schrodinger-Maxwell-Bloch equations (NLS-MBE), which describes the optical pulse propagation in an erbium doped fiber and find PT-symmetric and reverse space-time Schrodinger-Maxwell-Bloch equations, i.e. the kinds of nonlocal Schrodinger-Maxwell-Bloch equations. In particular case, the system of Schrödinger-Maxwell-Bloch equations is integrable by the Inverse Scattering Method as shown in the work of M.A blowitz and Z. Musslimani. Following this method we prove the integrability of the nonlocal system of Schröodinger-Maxwell-Bloch equations by Lax pairs. Also the explicit and different seed solutions are constructed by using Darboux transformation.

Research paper thumbnail of Initial conditions of pre-inflation with Hilltop potential in loop quantum cosmology

General Relativity and Gravitation

In this paper, we investigate the dynamics of pre-inflation with Hilltop potential in the framewo... more In this paper, we investigate the dynamics of pre-inflation with Hilltop potential in the framework of loop quantum cosmology. The initial conditions of inflaton field at the quantum bounce is categorized into two classes, first one is dominated by kinetic energy and second one by potential energy. In both cases, the physically viable initial values of inflaton field at the bounce are obtained numerically that generate the desired slow-roll inflation and also sufficient number of e-folds. To be consistent with observations at least 60 e-folds are required. In case of kinetic energy dominated initial conditions of inflaton field at the bounce, the numerical evolution of the background prior to preheating is divided into three different regions: bouncing, transition and slow-roll inflation whereas bouncing and transition phases disappear in the potential energy dominated case but still slow-roll inflation is achieved. This is true in case of p = 4 and v = 1M P l of Hilltop potential. However for other cases, slow-roll inflation can not be obtained. Moreover, we study the phase space analysis for Hilltop potential and discuss the phase space trajectories under the chosen parameters.

Research paper thumbnail of Generalized Heisenberg Ferromagnet type Equation and Modified Camassa-Holm Equation: Geometric Formulation, Soliton Solutions and Equivalence

arXiv: Exactly Solvable and Integrable Systems, 2020

We study the integrability and equivalence of a generalized Heisenberg ferromagnet-type equation ... more We study the integrability and equivalence of a generalized Heisenberg ferromagnet-type equation (GHFE). The different forms of this equation as well as its reduction are presented. The Lax representation (LR) of the equation is obtained. We observe that the geometrical and gauge equivalent counterpart of the GHFE is the modified Camassa-Holm equation (mCHE) with an arbitrary parameter kappa\kappakappa. Finally, the 1-soliton solution of the GHFE is obtained.

Research paper thumbnail of Soliton Surface for the (1+1)-Dimensional Schr{\"o}dinger-Maxwell-Bloch Equation

Geometry Integrability and Quantization

Research paper thumbnail of Initial conditions of pre-inflation with Hilltop potential in loop quantum cosmology

arXiv (Cornell University), Aug 12, 2021

In this paper, we investigate the dynamics of pre-inflation with Hilltop potential in the framewo... more In this paper, we investigate the dynamics of pre-inflation with Hilltop potential in the framework of loop quantum cosmology. The initial conditions of inflaton field at the quantum bounce is categorized into two classes, first one is dominated by kinetic energy and second one by potential energy. In both cases, the physically viable initial values of inflaton field at the bounce are obtained numerically that generate the desired slow-roll inflation and also sufficient number of e-folds. To be consistent with observations at least 60 e-folds are required. In case of kinetic energy dominated initial conditions of inflaton field at the bounce, the numerical evolution of the background prior to preheating is divided into three different regions: bouncing, transition and slow-roll inflation whereas bouncing and transition phases disappear in the potential energy dominated case but still slow-roll inflation is achieved. This is true in case of p = 4 and v = 1M P l of Hilltop potential. However for other cases, slow-roll inflation can not be obtained. Moreover, we study the phase space analysis for Hilltop potential and discuss the phase space trajectories under the chosen parameters.

Research paper thumbnail of Nonlocal Schrödinger-Maxwell-Bloch Equations

Journal of Physics: Conference Series, 2021

In this paper we research the (1+1)-dimensional system of Schrodinger-Maxwell-Bloch equations (NL... more In this paper we research the (1+1)-dimensional system of Schrodinger-Maxwell-Bloch equations (NLS-MBE), which describes the optical pulse propagation in an erbium doped fiber and find PT-symmetric and reverse space-time Schrodinger-Maxwell-Bloch equations, i.e. the kinds of nonlocal Schrodinger-Maxwell-Bloch equations. In particular case, the system of Schrödinger-Maxwell-Bloch equations is integrable by the Inverse Scattering Method as shown in the work of M.A blowitz and Z. Musslimani. Following this method we prove the integrability of the nonlocal system of Schröodinger-Maxwell-Bloch equations by Lax pairs. Also the explicit and different seed solutions are constructed by using Darboux transformation.

Research paper thumbnail of Initial conditions of pre-inflation with Hilltop potential in loop quantum cosmology

General Relativity and Gravitation

In this paper, we investigate the dynamics of pre-inflation with Hilltop potential in the framewo... more In this paper, we investigate the dynamics of pre-inflation with Hilltop potential in the framework of loop quantum cosmology. The initial conditions of inflaton field at the quantum bounce is categorized into two classes, first one is dominated by kinetic energy and second one by potential energy. In both cases, the physically viable initial values of inflaton field at the bounce are obtained numerically that generate the desired slow-roll inflation and also sufficient number of e-folds. To be consistent with observations at least 60 e-folds are required. In case of kinetic energy dominated initial conditions of inflaton field at the bounce, the numerical evolution of the background prior to preheating is divided into three different regions: bouncing, transition and slow-roll inflation whereas bouncing and transition phases disappear in the potential energy dominated case but still slow-roll inflation is achieved. This is true in case of p = 4 and v = 1M P l of Hilltop potential. However for other cases, slow-roll inflation can not be obtained. Moreover, we study the phase space analysis for Hilltop potential and discuss the phase space trajectories under the chosen parameters.

Research paper thumbnail of Generalized Heisenberg Ferromagnet type Equation and Modified Camassa-Holm Equation: Geometric Formulation, Soliton Solutions and Equivalence

arXiv: Exactly Solvable and Integrable Systems, 2020

We study the integrability and equivalence of a generalized Heisenberg ferromagnet-type equation ... more We study the integrability and equivalence of a generalized Heisenberg ferromagnet-type equation (GHFE). The different forms of this equation as well as its reduction are presented. The Lax representation (LR) of the equation is obtained. We observe that the geometrical and gauge equivalent counterpart of the GHFE is the modified Camassa-Holm equation (mCHE) with an arbitrary parameter kappa\kappakappa. Finally, the 1-soliton solution of the GHFE is obtained.

Research paper thumbnail of Soliton Surface for the (1+1)-Dimensional Schr{\"o}dinger-Maxwell-Bloch Equation

Geometry Integrability and Quantization