15014387
Construction of Special Solutions for Nonintegrable Dynamical Systems with the Help of the Painleve Analysis
The generalized Henon-Heiles system has been considered. In two nonintegrable cases with the help of the Painleve test new special solutions have been found as Laurent series, de- pending on three parameters. The obtained series converge in some ring. One of parameters determines the singularity point location, other parameters determine coefficients of series. For some values of these parameters the obtained Laurent series coincide with the Laurent series of the known exact solutions. The Painleve test can be used not only to construct local solutions as the Laurent series but also to find elliptic solutions.
118566695
Stable exact cosmological solutions in induced gravity models
We study dynamics of induced gravity cosmological models with the sixth degree polynomial potentials, that have found using the superpotential method. The important property of these models are existence of exact cosmological solutions that tend to fixed points. The stability of these cosmological solutions have been obtained. In particular, we find conditions under which solutions with a non-monotonic Hubble parameter that tend to a fixed point are attractors.
125533559
Nonlocal cosmological models and exact solutions
118914395
Stability of de Sitter Solutions in Non-local Cosmological Models
A non-local gravity model, which includes a function $f(\Box^{-1} R)$, where $\Box$ is the d'Alembert operator, is considered. For the model with an exponential $f(\Box^{-1} R)$ de Sitter solutions are explored, without any restrictions on the parameters. Using Hubble-normalized variables, the stability of the de Sitter solutions is investigated, with respect to perturbations in the Bianchi I metric, in the case of zero cosmological constant, and sufficient conditions for stability are obtained.
118725633
Integrable cosmological models with non-minimally coupled scalar fields
We obtain general solutions for some flat Friedmann universes filled with a scalar field in induced gravity models and models including the Hilbert–Einstein curvature term plus a scalar field conformally coupled to gravity. As is well known, these models are connected to minimally coupled models through the combination of a conformal transformation and a transformation of the scalar field. The explicit forms of the self-interaction potentials for six exactly solvable models are presented here. We obtain the general solution for one of the integrable models, namely, the induced gravity model with a power-law potential for the self-interaction of the scalar field. We argue that although being mathematically in a one-to-one correspondence with the solutions in the minimally coupled models, the solutions in the corresponding non-minimally coupled models are physically different. This is because the cosmological evolutions seen by an internal observer connected with the cosmic time can be quite different. The study of a few induced gravity models with particular potentials gives us an explicit example of such a difference.
115160895
Exact Solutions in Nonlocal Linear Models
A general class of cosmological models driven by a nonlocal scalar field inspired by the string field theory is studied. Using the fact that the considering linear nonlocal model is equivalent to an infinite number of local models we have found an exact special solution of the nonlocal Friedmann equations. This solution describes a monotonically increasing Universe with the phantom dark energy.
115548969
INVESTIGATION OF THE ELECTRON, NUCLEAR-ACTIVE, AND MUON COMPONENTS OF EXTENSIVE AIR SHOWERS.
118194329
STUDY OF RADIO EMISSION FROM EXTENSIVE AIR SHOWERS BY MEANS OF A SYSTEM OF HALF-WAVE DIPOLES IN THE COMPLEX ARRAY OF THE MOSCOW STATE UNIVERSITY.
121231645
Violation of scale invariance in hadron interactions at super-high energies
It is shown that, when the scaling in hadron interactions is valid at energies of about 2 x 10'*eV for x = 0.1-1.0 accurate within loo/& the extrapolation of the 'scaling model' to the super-high-energy range 1015-10'7 eV contradicts the experimental data on extensive air showers (EAS).
118415722
Multiplicity Distribution of the Particles Produced in Nuclear Interactions of High-Energy Cosmic Rays
125373617
One rigorous negative result in quantum field theory