117782897
HIGH-ENERGY MUONS IN 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.
117518082
Forbush effect in solar proton intensity
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).
35132848
Construction of Special Solutions for Nonintegrable Systems
Abstract The Painlevé test is very useful to construct not only the Laurent series solutions of systems of nonlinear ordinary differential equations but also the elliptic and trigonometric ones. The standard methods for constructing the elliptic solutions consist of two independent steps: transformation of a nonlinear polynomial differential equation into a nonlinear algebraic system and a search for solutions of the obtained system. It has been demonstrated by the example of the generalized Hénon–Heiles system that the use of the Laurent series solutions of the initial differential equation assists to solve the obtained algebraic system. This procedure has been automatized and generalized on some type of multivalued solutions. To find solutions of the initial differential equation in the form of the Laurent or Puiseux series we use the Painlevé test. This test can also assist to solve the inverse problem: to find the form of a polynomial potential, which corresponds to the required type of solutions. We consider the five–dimensional gravitational model with a scalar field to demonstrate this.
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.
14846577
Exactly Solvable SFT Inspired Phantom Model
An exact solution to the Friedmann equations with a string inspired phantom scalar matter field is constructed and the absence of the “Big Rip” singularity is shown explicitly. The notable features of the concerned model are a ghost sign of the kinetic term and a special polynomial form of the effective tachyon potential. The constructed solution is stable with respect to small fluctuations of the initial conditions and special deviations of the form of the potential.
119703497
Elliptic solutions of the quintic complex one-dimensional Ginzburg–Landau equation
The Conte–Musette method has been modified for the search of only elliptic solutions to systems of differential equations. A key idea of this a prior restriction is to simplify calculations by means of the use of a few Laurent-series solutions instead of one and the use of the residue theorem. The application of this approach to the quintic complex one-dimensional Ginzburg–Landau equation (CGLE5) allows us to find elliptic solutions in the wave form. Restrictions on coefficients, which are necessary conditions for the existence of elliptic solutions for the CGLE5, have been found as well. We demonstrate that to find elliptic solutions the analysis of a system of differential equations is preferable to the analysis of the equivalent single differential equation.
895
Construction of Single-valued Solutions for Nonintegrable Systems with the Help of the Painleve Test
The Painleve test is very useful to construct not only the Laurent-series solutions but also the elliptic and trigonometric ones. Such single-valued functions are solutions of some polynomial first order differential equations. To find the elliptic solutions we transform an initial nonlinear differential equation in a nonlinear algebraic system in parameters of the Laurent-series solutions of the initial equation. The number of unknowns in the obtained nonlinear system does not depend on number of arbitrary coefficients of the used first order equation. In this paper we describe the corresponding algorithm, which has been realized in REDUCE and Maple.