93 citations · 354 across the 13 of their papers we have counts for
13 papers
Integrable Motion of Curves in Self-Consistent Potentials : Relation to Spin Systems and Soliton Equations
R. Myrzakulov, G. K. Mamyrbekova, G. N. Nugmanova +2
Motion of curves and surfaces in lead to nonlinear evolution equations which are often integrable. They are also intimately connected to the dynamics of spin chains in the c…
Darboux Transformation and Exact Solutions of the integrable Heisenberg ferromagnetic equation with self-consistent potentials
Z. S. Yersultanova, M. Zhassybayeva, K. Yesmakhanova +2
Integrable Heisenberg ferromagnetic equations are an important subclass of integrable systems. The M-XCIX equation is one of a generalizations of the Heisenberg ferromagnetic equat…
Integrable (2+1)-Dimensional Spin Models with Self-Consistent Potentials
R. Myrzakulov, G. Mamyrbekova, G. Nugmanova +1
Integrable spin systems possess interesting geometrical and gauge invariance properties and have important applications in applied magnetism and nanophysics. They are also intimate…
Integrable Heisenberg Ferromagnet Equations with self-consistent potentials
Zh. Kh. Zhunussova, K. R. Yesmakhanova, D. I. Tungushbaeva +3
In this paper, we consider some integrable Heisenberg Ferromagnet Equations with self-consistent potentials. We study their Lax representations. In particular we give their equival…
Periodic Cosmological Evolutions of Equation of State for Dark Energy
Kazuharu Bamba, Ujjal Debnath, Kuralay Yesmakhanova +3
We demonstrate two periodic or quasi-periodic generalizations of the Chaplygin gas (CG) type models to explain the origins of dark energy as well as dark matter by using the Weiers…
FRW cosmological models with integrable and nonintegrable differential equations of state
Shynaray Myrzakul, Kuralay Esmakhanova, Kairat Myrzakulov +2
The basic models of modern cosmology work in FRW spacetime. Hence follows that it is important to study the physical and mathematical nature of FRW cosmological models. In this wor…
Reconstruction of f-essence and fermionic Chaplygin gas models of dark energy
P. Tsyba, K. Yerzhanov, K. Esmakhanova +3
Recently, it was proposed a new fermionic model of dark energy, the so-called f-essence. In this work, we explicitly reconstruct the different f-essence models. In particular, thes…
Dark energy in some integrable and nonintegrable FRW cosmological models
Kuralay Esmakhanova, Nurgissa Myrzakulov, Gulgasyl Nugmanova +3
One of the greatest challenges in cosmology today is to determine the nature of dark energy, the sourse of the observed present acceleration of the Universe. Besides the vacuum ene…
A note on the relationship between solutions of Einstein, Ramanujan and Chazy equations
Kuralay Esmakhanova, Yerlan Myrzakulov, Gulgasyl Nugmanova +1
The Einstein equation for the Friedmann-Robertson-Walker metric plays a fundamental role in cosmology. The direct search of the exact solutions of the Einstein equation even in thi…
G-essence cosmologies with scalar-fermion interactions
O. V. Razina, Y. M. Myrzakulov, N. S. Serikbayev +3
We study the two particular models of g-essence with Yukawa type interactions between a scalar field and a classical Dirac field . For the homogeneous, isotropic and flat Fr…
Einstein-Cartan gravity with scalar-fermion interactions
Olga Razina, Yerlan Myrzakulov, Nurzhan Serikbayev +2
In this paper, we have considered the g-essence and its particular cases, k-essence and f-essence, within the framework of the Einstein-Cartan theory. We have shown that a single f…
On the Integrable Generalization of the 1D Toda Lattice
P. Yu. Tsyba, K. R. Esmakhanova, G. N. Nugmanova +1
A generalized Toda Lattice equation is considered. The associated linear problem (Lax representation) is found. For simple case N=3 the -function Hirota form is presented that a…
A (2+1) dimensional integrable spin model: Geometrical and gauge equivalent counterpart, solitons and localized coherent structures
R. Myrzakulov, S. Vijayalakshmi, G. N. Nugmanova +1
A non-isospectral (2+1) dimensional integrable spin equation is investigated. It is shown that its geometrical and gauge equivalent counterparts is the (2+1) dimensional nonlinear…