125 research outputs found
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, depending 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.Comment: 8 pages, to appear in the proceedings of the Fifth International
Conference "Symmetry in Nonlinear Mathematical Physics" (Kiev, Ukraine, June
23-29, 2003) http://www.imath.kiev.ua/~appmath/conf.htm
Construction of solutions for the generalized Henon-Heiles system with the help of the Painleve test
The Henon-Heiles system in the general form has been considered. In a
nonintegrable case with the help of the Painleve test new solutions have been
found as formal Laurent or Puiseux series, depending on three parameters. One
of parameters determines a location of the singularity point, other parameters
determine coefficients of series. It has been proved, that if absolute values
of these two parameters are less or equal to unit, then obtained series
converge in some ring. For some values of these parameters the obtained Laurent
series coincide with the Laurent series of the known exact solutions.Comment: LaTeX2e, 16 p
The Painleve Analysis and Special Solutions for Nonintegrable Systems
The H\'enon--Heiles system in the general form is studied. In a nonintegrable
case new solutions have been found as formal Laurent series, depending on three
parameters. One of parameters determines a location of the singularity point,
other parameters determine coefficients of the Laurent series. For some values
of these two parameters the obtained Laurent series coincide with the Laurent
series of the known exact solutions.Comment: LaTeX2e, 14 p
Cosmological Solutions in Nonlocal Models
A non-local modified gravity model with an analytic function of the
d'Alembert operator that has been proposed as a possible way of resolving the
singularities problems in cosmology is considered. We show that the anzats that
is usually used to obtain exact solutions in this model provides a connection
with gravity models.Comment: 5 page
Irreducibility of the set of field operators in Noncommutative Quantum Field Theory
Irreducibility of the set of quantum field operators has been proved in
noncommutative quantum field theory in the general case when time does not
commute with spatial variables.Comment: 6 page
Renormalization-group improved inflationary scenarios
The possibility to construct an inflationary scenario for
renormalization-group improved potentials corresponding to the Higgs sector of
quantum field models is investigated. Taking into account quantum corrections
to the renormalization-group potential which sums all leading logs of
perturbation theory is essential for a successful realization of the
inflationary scenario, with very reasonable parameters values. The scalar
electrodynamics inflationary scenario thus obtained are seen to be in good
agreement with the most recent observational data
Induced gravity models with exact bounce solutions
We study dynamics of induced gravity cosmological models with the sixth
degree polynomial potentials, that have been constructed using the
superpotential method. We find conditions on the potential under which exact
bounce solutions exist and study the stability of these solutions.Comment: 6 page
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.Comment: 4 pages, to appear in the proceedings of the seventh International
Workshop "Supersymmetries and Quantum Symmetries" (SQS'07), Dubna, Russia,
July 30 - August 4, 2007, http://theor.jinr.ru/~sqs07
Crossing of the w=-1 Barrier by D3-brane Dark Energy Model
We explore a possibility for the Universe to cross the w=-1 cosmological
constant barrier for the dark energy state parameter. We consider the Universe
as a slowly decaying D3-brane. The D3-brane dynamics is approximately described
by a nonlocal string tachyon interaction and a back reaction of gravity is
incorporated in the closed string tachyon dynamics. In a local effective
approximation this model contains one phantom component and one usual field
with a simple polynomial interaction. To understand cosmological properties of
this system we study toy models with the same scalar fields but with modified
interactions. These modifications admit polynomial superpotentials. We find
restrictions on these interactions under which it is possible to reach w=-1
from below at large time. Explicit solutions with the dark energy state
parameter crossing/non-crossing the barrier w=-1 at large time are presented.Comment: LaTeX, 21 pages, 4 figures, references adde
Analytical vectors and a new criterion of regularity for representation of canonical commutation relations algebra
New criterion of regularity for representation of canonical commutation
relations algebra is given on the basis of concept of an analytical vector.Comment: 5 pages, The XIXth International Workshop on High Energy Physics and
Quantum Field Theory 8-15 September 2010 Golitsyno, Moscow, Russi
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