641 research outputs found
Some properties of small perturbations against a stationary solution of the nonlinear Schrodinger equation
In this paper, classical small perturbations against a stationary solution of
the nonlinear Schrodinger equation with the general form of nonlinearity are
examined. It is shown that in order to obtain correct (in particular, conserved
over time) nonzero expressions for the basic integrals of motion of a
perturbation even in the quadratic order in the expansion parameter, it is
necessary to consider nonlinear equations of motion for the perturbations. It
is also shown that, despite the nonlinearity of the perturbations, the
additivity property is valid for the integrals of motion of different nonlinear
modes forming the perturbation (at least up to the second order in the
expansion parameter).Comment: 20 pages, v4: title changed; Introduction and Conclusion modified;
main text slightly enlarged; references added; typos correcte
Bulk metric of brane world models and submanifolds in 6D pseudo-Euclidean space-time
In this short note, five-dimensional brane world models with dS_{4} metric on
the branes are discussed. The explicit coordinate transformations, which show
the equivalence between the bulk metric of these brane world models and the
metric induced on an appropriate submanifolds in the flat six-dimensional
pseudo-Euclidean space-time, are presented. The cases of the zero and non-zero
cosmological constant in the bulk are discussed in detail.Comment: 5 pages, typos correcte
The strong coupling effect and auxiliary fields in the DGP-model
The DGP-model with additional terms in the action is considered. These terms
have a special form and include auxiliary scalar fields without kinetic terms,
which are non-minimally coupled to gravity. The use of these fields allows one
to exclude the mode, which corresponds to the strong coupling effect, from the
theory. Effective four-dimensional theory on the brane appears to be the same,
as in the original DGP-model.Comment: 9 pages, LaTe
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