It is shown that the inflationary model is the result of the symmetry of the generalized F(R, T, X, ϕ)-cosmological model using the Noether symmetry. It leads to a solution, a particular case of which is Starobinsky’s cosmological model. It is shown that even in the more particular case of cosmological models F(R, X, ϕ) and F(T, X, ϕ) the Monge–Ampère equation is still obtained, ...

We investigated the gravity model F (R, T), which interacts with a fermion field in a uniform and isotropic flat spacetime FLRW. The main idea and purpose of the work done was to create a mathematical model and find a particular solution for the scale factor a, since it describes the dynamics of the evolution of the Universe. The solutions for this universe are obtained using ...

Yerzhanov, K.; Bauyrzhan, G.; Altaibayeva, A.; Myrzakulov, R. Inflation from the Symmetry of the Generalized Cosmological Model. Symmetry 2021, 13, 2254. https:// doi.org/10.3390/sym13122254

In recent years, symmetry in abstract partial differential equations has found wide application in the field of nonlinear integrable equations. The symmetries of the corresponding transformation groups for such equations make it possible to significantly simplify the procedure for establishing equivalence between nonlinear integrable equations from different areas of physics, which ...

The goal of this paper is to study new cosmological models where the dark energy is a varying Chaplygin gas. This specific dark energy model with non-linear EoS had been often discussed in modern cosmology. Contrary to previous studies, we consider new forms of nonlinear non-gravitational interaction between dark matter and assumed dark energy models. We applied the phase space ...

In this paper, we study the generalized Heisenberg ferromagnet equation, namely, the M-CVI equation. This equation is integrable. The integrable motion of the space curves induced by the M-CVI equation is presented. Using this result, the Lakshmanan (geometrical) equivalence between the M-CVI equation and the two-component CamassaHolm equation is established.

The goal of this paper is to study new cosmological models where the dark energy is a varying Chaplygin gas. This specific dark energy model with non-linear EoS had been often discussed in modern cosmology. Contrary to previous studies, we consider new forms of nonlinear non-gravitational interaction between dark matter and assumed dark energy models. We applied the phase space ...

In recent years, symmetry in abstract partial differential equations has found wide application in the field of nonlinear integrable equations. The symmetries of the corresponding transformation groups for such equations make it possible to significantly simplify the procedure for establishing equivalence between nonlinear integrable equations from different areas of physics, which ...

It is shown that the inflationary model is the result of the symmetry of the generalized F(R, T, X, ϕ)-cosmological model using the Noether symmetry. It leads to a solution, a particular case of which is Starobinsky’s cosmological model. It is shown that even in the more particular case of cosmological models F(R, X, ϕ) and F(T, X, ϕ) the Monge–Ampère equation is still obtained, ...

In recent years, symmetry in abstract partial differential equations has found wide application in the field of nonlinear integrable equations. The symmetries of the corresponding transformation groups for such equations make it possible to significantly simplify the procedure for establishing equivalence between nonlinear integrable equations from different areas of physics, which ...