15559352
Construction of doubly periodic solutions via the Poincare–Lindstedt method in the case of massless ϕ4 theory
Doubly periodic (periodic both in time and in space) solutions for the Lagrange–Euler equation of the (1+1)-dimensional scalar ϕ4 theory are studied. Provided that the nonlinear term is small, the Poincare–Lindstedt asymptotic method can be used to find asymptotic solutions in the standing wave form. The principal resonance problem, which arises for zero mass, is solved if the leading-order term is taken in the form of Jacobi elliptic function. To obtain this leading-order term the system REDUCE is used.
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.
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
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.
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.
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.