6 research outputs found
Meromorphic traveling wave solutions of the complex cubic-quintic Ginzburg-Landau equation
We look for singlevalued solutions of the squared modulus M of the traveling
wave reduction of the complex cubic-quintic Ginzburg-Landau equation. Using
Clunie's lemma, we first prove that any meromorphic solution M is necessarily
elliptic or degenerate elliptic. We then give the two canonical decompositions
of the new elliptic solution recently obtained by the subequation method.Comment: 14 pages, no figure, to appear, Acta Applicandae Mathematica
Stringy Dark Energy Model with Cold Dark Matter
Cosmological consequences of adding the Cold Dark Matter (CDM) to the exactly
solvable stringy Dark Energy (DE) model are investigated. The model is
motivated by the consideration of our Universe as a slowly decaying D3-brane.
The decay of this D-brane is described in the String Field Theory framework.
Stability conditions of the exact solution with respect to small fluctuations
of the initial value of the CDM energy density are found. Solutions with large
initial value of the CDM energy density attracted by the exact solution without
CDM are constructed numerically. In contrast to the LambdaCDM model the Hubble
parameter in the model is not a monotonic function of time. For specific
initial data the DE state parameter w_{DE} is also not monotonic function of
time. For these cases there are two separate regions of time where w_{DE} being
less than -1 is close to -1.Comment: 15 pages, 6 figures; references adde
Cosmological perturbations in SFT inspired non-local scalar field models
We study cosmological perturbations in models with a single non-local scalar
field originating from the string field theory description of the rolling
tachyon dynamics. We construct the equation for the energy density
perturbations of the non-local scalar field and explicitly prove that for the
free field it is identical to a system of local cosmological perturbation
equations in a particular model with multiple (maybe infinitely many) local
free scalar fields.Comment: 21 pages, no figures, v3: presentation improved, results unchanged,
references adde
Global stability analysis for cosmological models with nonminimally coupled scalar fields
We explore dynamics of cosmological models with a nonminimally coupled scalar field evolving on a spatially flat Friedmann-Lemaître-Robertson-Walker background. We consider cosmological models including the Hilbert-Einstein curvature term and the N degree monomial of the scalar field nonminimally coupled to gravity. The potential of the scalar field is the n degree monomial or polynomial. We describe several qualitatively different types of dynamics depending on values of power indices N and n. We identify that three main possible pictures correspond to n2N cases. Some special features connected with the important cases of N=n (including the quadratic potential with quadratic coupling) and n=2N (which shares its asymptotics with the potential of the Higgs-driven inflation) are described separately. A global qualitative analysis allows us to cover the most interesting cases of small N and n by a limiting number of phase-space diagrams. The influence of the cosmological constant to the global features of dynamics is also studied. © 2014 American Physical Society
Global stability analysis for cosmological models with nonminimally coupled scalar fields
We explore dynamics of cosmological models with a nonminimally coupled scalar field evolving on a spatially flat Friedmann-Lemaître-Robertson-Walker background. We consider cosmological models including the Hilbert-Einstein curvature term and the N degree monomial of the scalar field nonminimally coupled to gravity. The potential of the scalar field is the n degree monomial or polynomial. We describe several qualitatively different types of dynamics depending on values of power indices N and n. We identify that three main possible pictures correspond to n2N cases. Some special features connected with the important cases of N=n (including the quadratic potential with quadratic coupling) and n=2N (which shares its asymptotics with the potential of the Higgs-driven inflation) are described separately. A global qualitative analysis allows us to cover the most interesting cases of small N and n by a limiting number of phase-space diagrams. The influence of the cosmological constant to the global features of dynamics is also studied. © 2014 American Physical Society