25,860 research outputs found
Geometrical resonance in spatiotemporal systems
We generalize the concept of geometrical resonance to perturbed sine-Gordon,
Nonlinear Schrödinger and Complex Ginzburg-Landau equations. Using this
theory we can control different dynamical patterns. For instance, we can
stabilize breathers and oscillatory patterns of large amplitudes successfully
avoiding chaos. On the other hand, this method can be used to suppress
spatiotemporal chaos and turbulence in systems where these phenomena are
already present. This method can be generalized to even more general
spatiotemporal systems.Comment: 2 .epl files. Accepted for publication in Europhysics Letter
Dynamics of a Self-interacting Scalar Field Trapped in the Braneworld for a Wide Variety of Self-interaction Potentials
We apply the dynamical systems tools to study the linear dynamics of a
self-interacting scalar field trapped in the braneworld, for a wide variety of
self-interaction potentials. We focus on Randall-Sundrum (RS) and on
Dvali-Gabadadze-Porrati (DGP) braneworld models exclusively. These models are
complementary to each other: while the RS brane produces ultra-violet (UV)
corrections to general relativity, the DGP braneworld modifies Einstein's
theory at large scales, i. e., produces infra-red (IR) modifications of general
relativity. This study of the asymptotic properties of both braneworld models,
shows -- in the phase space -- the way the dynamics of a scalar field trapped
in the brane departs from standard general relativity behaviour.Comment: 12 pages, 5 figures and 5 table
On algebraic classification of quasi-exactly solvable matrix models
We suggest a generalization of the Lie algebraic approach for constructing
quasi-exactly solvable one-dimensional Schroedinger equations which is due to
Shifman and Turbiner in order to include into consideration matrix models. This
generalization is based on representations of Lie algebras by first-order
matrix differential operators. We have classified inequivalent representations
of the Lie algebras of the dimension up to three by first-order matrix
differential operators in one variable. Next we describe invariant
finite-dimensional subspaces of the representation spaces of the one-,
two-dimensional Lie algebras and of the algebra sl(2,R). These results enable
constructing multi-parameter families of first- and second-order quasi-exactly
solvable models. In particular, we have obtained two classes of quasi-exactly
solvable matrix Schroedinger equations.Comment: LaTeX-file, 16 pages, submitted to J.Phys.A: Math.Ge
A New Algebraization of the Lame Equation
We develop a new way of writing the Lame Hamiltonian in Lie-algebraic form.
This yields, in a natural way, an explicit formula for both the Lame
polynomials and the classical non-meromorphic Lame functions in terms of
Chebyshev polynomials and of a certain family of weakly orthogonal polynomialsComment: Latex2e with AMS-LaTeX and cite packages; 32 page
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