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 $f(R)$ gravity models.Comment: 5 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

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

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