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

Brane induced gravity in warped backgrounds and the absence of the radion

A model with brane-localized curvature terms in a warped background is proposed. The model is based on the Randall-Sundrum solution for the background metric and possesses some interesting features, in particular, the radion field is absent in it. Although there is no modification of gravity at long distances, the model predicts deviations from Newton's law at short distances. This effect can be observed in the experiments for testing gravity at sub-millimeter scales.Comment: LaTeX, 11 pages, corrected typos. Accepted to Nuclear Physics

On the long-range gravity in warped backgrounds

In this paper the Randall-Sundrum model with brane-localized curvature terms is considered. Within some range of parameters a compact extra dimension in this model can be astronomically large. In this case the model predicts small deviation from Newton's law at astronomical scales, caused by the massive modes. The existence of this deviation can result in a slight affection on the planetary motion trajectories.Comment: LaTeX, 9 pages, typos corrected, reference adde